Bismillah al-Rahman al-Rahim
“And He it is Who created the heavens and the earth in six days (periods/phases)....” (Qur'an 11:7) 
Time has a mysterious existence, a nature that is, as yet, unfathomable to us. It does not have any immediately evident, firmly graspable reality such as that found in material objects (and even our understanding of matter succumbs to mystery as we peer deeper into its innermost structures).
Time has variously been regarded as “a dimension in which events occur in sequence” or else as a “mental measuring system” rather than a dimension or an objective thing having its own independent reality. It has sometimes been viewed as a way consciousness has of measuring motion or change (with the (Qur'anic) proviso that everything in existence has some degree of consciousness (some way of interfacing with and perceiving or detecting it's surroundings), however infinitesimally minute). Our consciousness of time exists primarily as a retention in memory and an anticipation of the future since the immediate now (the present moment) is of ungraspable granularity. It slips away even as we experience it. No matter how finely we slice our measurement of time (into nano or pico seconds), there is never an instant we can claim as now since each moment is endlessly sliding away leaving only an imprint in our memory and an anticipation of the moment still to come. We only see what has slipped past and wait for what we project into the future, but can never grasp the present moment although we may have an illusion of doing so because of the retention of a succession of moments in our memory like the persistence of vision. And it is the constant slipping, the endless change from moment to moment in external and internal worlds that makes possible our perception of time - the awareness of the difference between one instant and another.
Our perception of time's attributes and characteristics can vary, depending on the motion of things and their relationship and interaction with one another (time exhibits a quality of relativity). Our own circumstances, the region of space we inhabit, the motion inherent in the system we inhabit and interact with, and the link between our individual consciousness and the larger societal consciousness that surrounds and impacts us - all of these have a bearing on time and our subjective perception of it.
According to Mulla Sadra “...time is not an independent realm for things and phenomena, so that is has a separate existence and temporal things are contained in it. Rather, like the volume of a body, it (time) is an essential and internal characteristic of body, and naturally, every phenomena, will possess a specific time for itself which is considered to be an aspect of its existence.” (Amuzish Falsafah) So each object is wrapped in its own cloak of time and space and if our perception of time was sufficiently keen we would be individually aware that we each possess our own specific experience of time. Nevertheless, humans on earth share a sufficiently close proximity and similarity such that we experience a common way of measuring time - we share a more or less common idea of what constitutes a day based on characteristics of our local environment (e.g., the period of rotation of the earth). However, there are strange pointers in the Qur'an, that appeal to us to transcend the common view of what constitutes time. These indicate that time and it's perception varies greatly not just within the material universe but across levels and gradations of reality. It is possible for humans, whose being is capable of spanning different realms, to experience these different gradations (such as the experience of the Prophet during his mir'aj - his ascension).
While some of the Qur'an's verses emphasize our shared sense of time and the orderliness visible in the universe, other verses hint at the limits of our understanding and point to borders beyond which a transformation of the order and patterns that we take for granted occurs. Certain verses provide oblique metaphysical glimpses of this shift in time and its perception. For example, the Qur'an speaks of “a day whose measure is a thousand years of what you count.” (Qur'an 22:47) and of “a day whose measure is fifty thousand years.” (Qur'an 70:4) It also speaks of a day so short as to be immeasurable - this is yawm al-sha'n, the day of the task - “And in every day (moment/instant) He exercises universal power” (Qur'an 55:29).
Note: In a hadith, the Prophet says that in the time of al-Dajjal (an anti-christ like figure) there will be “a day like a year, a day like a month, a day like a week, and the rest of his days are like your days.” So in our own world, time or its perception or the interpretation of time and our perception of time during the period of the dajjal's manifestation may seem to transform and change. Or, an alternate interpretation may be that the appearance of the Dajjal in this world occurs gradually, like a slow but accelerating descent away from the divine. As the metaphysical underpinnings of religion weaken and humankind's connection with the divine fades into the realm of myth and skepticism, a Dajjal-like system begins to manifest and its elements strengthen and solidify over time until eventually it establishes and manifests powerfully in this world (“the rest of his days are like your days”) establishing its dominance and the apparent overthrow of all genuine religious systems.
As well, the Prophet (s.a.) and his awliya (a.s.) speak of other realms (levels of reality) in which time and being have an altered aspect and in which they exhibit metamorphosed qualities. So there is a higher archetypal world exhibiting a flow of time, “...dimensions, and extent other than that of the material sensible world. Infinite are its marvels, countless its cities, each with a thousand gates. They are peopled by countless (intelligent) creatures who are not even aware that God has created terrestrial Adam and his posterity....” In these cities “seven million languages are spoken, each different from the other....seventy thousand communities dwell in the city called Jabalqa. Not one among them but symbolizes with (and indicates the existence of) some community in this lower universe....” (Hadith from Hasan and Husayn)
So each level of existence, each realm, has it's own “day”. Which day the days of creation correspond to we do not know, which is why many translators render it as six periods of creation, in which each period is an unknown length of time during which an emergent process engendered, sustained, and suffused with God's creative command is at work. Time flows at a different rate, with an altered quality, within each realm. Each realm has not only its own quantitative time but also differs in the essential quality and priority of what exists within it. 
The other question that arises is why it refers to six periods. Why six? No really definitive answer can be given to this beyond a reference to other verses which mention the days of creation. However, symbolic congruences with the six days have been suggested by some commentators. One such congruence (suggested by Ibn Arabi's writings) is that human beings journey through six realms, six levels of existence. Their creation, life, death, and afterlife offers the possibility of travel through six matrices involving different manifestations of human life across different levels of reality. Within these there are many sub realms, but in general, there are six dominions, six demarcated levels and intervals in which human existence can manifest in some manner and in which different intensities of the experience of reality occurs, and in which time manifests in varying ways.
The first is the pre-existence in which every configuration of the human soul destined to be born in this universe was drawn out from Adam and brought before God Who asked them, “Am I not your Lord?”
“And when your Lord brought forth from the children of Adam...all their descendants, and made them bear witness against their own souls: Am I not your Lord? They said: Yes! we bear witness. Lest you should say on the day of resurrection: Surely we had no inner knowledge of this.” (Qur'an 7:172)
This indicates a pre-existence at some level for every human being who has ever been born or ever will be born. The recognition of God's Lordship lies in the original human nature (the fitra) since God took this shahada (testimony/witness) affirming His Lordship from all human beings before they entered into existence on the earth. They are asked, “Am I not your Lord?” and they affirm God's Lordship. So this recognition and affirmation is woven into a human being's very substance. The implication is that everyone who is born into this world has agreed in substance (in the essence of their soul) to this covenant, and that although we may have no conscious knowledge or memory of this pact, its reality is woven into our very nature. This world is a place of distraction and forgetfulness but at our core lies the metaphysical truth of this covenant and one of the purposes of religion is to awaken to consciousness an awareness of this bond between God and man as well as all the concealed potentials that flow from this bond.
The second world is the universe in which we now live. This is the world where we write the book of our individual lives. Death will lift us out from this world.
The Third is the world of the barzakh, also known as the world of the lesser resurrection or the world of the grave - it is one in which the human soul tastes its own nature and inner reality.
The fourth world is the world of the greater resurrection - when we awaken on an earth that has been remade, spread out, and extended to accommodate every creature that ever existed and to usher in the judgement. It is a world illuminated by the light of clear and deep perception so that every soul perceives in a penetrating manner its own reality and the realities underlying its every action.
The fifth world is the world of paradise and ghenna, the world in which actions and natures and their consequences return to their owners and only God's mercy provides relief.
The sixth world is the heights/the raised places (upon the dunes) a place elevated above paradise - “...and on the most elevated places there shall be men who know all by their marks....” (Qur'an 7:46-48) - this is a place of intimate proximity to God and for those granted special insight.
In each of these worlds there are lesser realms, and realms within realms but in general there are six broad categories and levels.
Each one has its own unique days, its own unique measure of time. So this is one possible indication of some congruence with the six days of creation - human existence in its totality maps onto the various levels of reality through which the human essence can journey.
But this present world in which we are now living was created as the place of trial, testing, and responsibility - so it is (as Ibn Arabi indicates) with our conduct here that we have to concern ourselves. The many levels of existence are all part of the totality of human existence - but, as the verse says, the crux of it is within this realm of testing, that He might “...determine which of you has the most beautiful conduct (actions).” (Qur'an 11:7)
Note: In some verses the Qur'an enumerates the breakdown of the six days (a total of four for the creation of the “earth” and what is in it, and two for the “heavens” and what is in them (Qur'an 41:9-12). The two periods for the heavens would then perhaps encompass the heaven of the covenant, and the seven heavens of the gardens of paradise. The four periods for the earth would perhaps encompass this material universe (including our earth), the earth of the barzakh, the earth of the resurrection (of judgement day), and the earth of the dunes (the elevated heights). However, all interpretation is at best nothing more than speculation and possibility and most commentators refrain from any absolute mapping out of the six days of creation.
Note: Another (esoteric) interpretation of the six days of creation includes a seventh day in which the purpose of creation is revealed and fulfilled - the seventh day is said to be alluded to in the ascension to the throne which follows the process of creation. “Lo! Your Lord is God Who created the heavens and the earth in six days. Then He ascended the Throne...” (Qur’an 7:54) This interpretation is detailed by Shafique Virani in his paper “The Days of Creation in the thought of Nasir Khusraw”. He writes that according to Khusraw... “This account of the genesis of the cosmos, shared by the Abrahamic faiths, does not concern the creation of the physical universe. Rather, the tradition refers to the genesis of a spiritual cosmos governed by God’s emissaries. This creation commenced with Adam, who represented the first day...and continued with Noah, Abraham, Moses and Jesus....The cycles of creation were brought to their completion by Muhammad....Yet to come was the last and final day (the sign of which is the advent of the Mehdi), which would consummate the entire spiritual creation. This was the...cycle of the Lord of the Resurrection or Qa’im-i qiyamat. It is through the Lord of the Resurrection that the divine unity and grandeur of God would be revealed and the purpose of creation fulfilled.”
Note: “Some notions of time say that it is cyclical while others say that it is linear. With the Linear conception, there is a starting point, a progression, and then a terminal point. On the surface, it would seem that Islam and the other Abrahamic traditions strictly adhere to the linear conception. You have the creation of the world which takes its own course until the saa`ah arrives, which terminates the world....(but) in the esoteric traditions of all religions, there's the idea of eternal cycles. Even the Qur'an conveys this idea: “Thou makest the night to pass into the day and Thou makest the day to pass into the night, and Thou bringest forth the living from the dead and Thou bringest forth the dead from the living.” (Qur'an 3:27). This is the sunna of Allah.
“There is also the idea of qualitative and quantitative time. Quantitative time is measured by the movement of electrons etc and is measured in relation to the movement of objects. In other words, there's a quantifiable progression. Qualitative time says that in addition to being quantitative, time has quality or ideas and these ideas penetrate from the higher world world to the lower one, and depending on how they penetrate makes the "when." The sequence in which they penetrate into the lower world gives you the illusion that there's actually a progress ( i.e. that events have a before and an after and that we are somehow going forward in time)....(in this case) time is not measured in a regression or succession but is measured by the things in it, the highest thing being the first thing. Therefore, if the spirit of the Prophet(s) is the highest creation of Allah, then metaphysically, it has to be the first.” (-Shuja Mirza)