Time has many different faces. One word, multiple meanings. Merriam-Webster on line dictionary[1] describes above 20 different flavours of the word "time". The most popular understanding is: "the thing that is measured as seconds, minutes, hours, days, years, etc" which is more like Newton's measure of duration.
A different use of word time is to express multiplicity of occurrences.You can do things once, twice, but not trice. It has to be three times. Not all languages have this association of time and multiplicity. In Slavic languages the word "raz" means more or less a unity and it is used in combination with a number from 2 onwards. It looks like it was once more obvious for some ancestors to associate multiplicity with repetition of events occurring in time rather then with a number of objects of the same kind.
My particular interest in time is: "The continued progress of existence as affecting people and things"[2].
This goes beyond a simple measure. This is the space for events to
happen and the mode of our existence in which we also perceive existence
of things other than ourselves, unless this is all one big illusion.
For a physicist time is a variable t and numbers that can be assigned to it. Experimentally, that would correspond to some clock indication as per Einstein's definition. It is interesting, how does then t relate to the progress of existence?
Finally time despite its operational definition given by Einstein is postulated to exist beyond clocks in the form of space-time continuum. So in my view then clocks as devices must be affected by the flow of local time. I do not like the concept of flow of time, in particular time that is a driving force of the clock, in the same way I would not like to say that inertial motion can sustain only due to a force.
The progress of existence like life of everyone of us appears to be in one direction only while other things progress in repetitive cycles such as grandfather's mechanical watch or a toy train on closed loop tracks. This is of course a simplistic view as none of the cycles can be exactly the same. There is always at least a tiny disturbance that makes each cycle different from the previous one.
The irreversibility of physical processes made British astronomer Arthur Eddington creating the concept of "the arrow of time"[3]. The term is now widely used. Why time has to have an arrow or a direction?
This is a convention by which we allow clocks to increase the number of second minutes etc. in an increasing order. We could equally build the clocks that count down rather than up and the world would not be any different. There is nothing unique about that. The direction is arbitrary yet some believe it may change.
If one recalls Newton's definition of time, it flows (where?,when?) and the flow has to have a direction.
The question is, where is time? Is that direction the same everywhere? Is it changing with distance,speed,gravity? Arrows shot from the bow generally don't change direction but they could turn around with gusts of wind. Can time do the same?
I am highly skeptical about the time arrow concept because time that is poorly defined in science appears to be made responsible for the direction of physical processes while each process generally is directed due to initial conditions and continues in a direction due to some form of force or inertia.
The questions whether time travel is possible and whether spontaneous processes can revert their direction is not yet answered by science although such claims are frequently made. At least that gives us some space for discussions.
[1]"Time." Merriam-Webster.com. Merriam-Webster, 6 July 2014. http://www.merriam-webster.com/dictionary/time
[2]"Time." www.oxforddictionaries.com. 6 July 2014.http://www.oxforddictionaries.com/definition/english/time
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