Time is an important concept in physics, but physics itself dosn't have that much to say about the why of time. Time shows up as a variable in most of the more complex physics equations, because often when you want to model something, you want to model something traveling through time.
Many such equations are "time symmetric", which means they work equally well for positive and negative values of time. If you plug a negative time value into the equations which define a black hole, you get a white hole (from which energy in indefinitely expelled rather then absorbed). It's not at all clear how you might get a white hole to appear in the actual universe, but if we find one we have the math to describe it. Most astrophysicists believe their existence is impossible, since despite that the math can deal with negative time values, they believe the universe cannot.
Perhaps more interestingly, if you plug a negative time value into the equations which define an electron (or any particle of matter) you get a particle which behaves basically like a positron (or whatever the corresponding anti-matter particle would be). We have found positrons and other anti-matter particles, which could (according to the math) just be normal matter particles traveling backwards in time.
So in most equations time can be treated as just another variable (which also means it can be graphed as just another dimension). It could actually be a vector of however many dimensions we wish, but we only notice time proceeding in one direction so it's almost always just treated as a scaler. The direction we always notice time proceeding in is always the direction which entropy increases, suggesting that our experience of time is highly related to the notion of entropy (though I at least have few ideas asto why this may be).
Another idea closely associated with time in most physicists mind is that of 'causality'. We really want to be able to say "one thing causes another," and we further want the cause to proceed the effect (i.e come before the effect according to our notion of time). Sadly, this is really more of a bookeeping convenience then anything else. You could, for example, say a forward time traveling positron heading north strikes a barrier which causes it to change direction so it is then traveling east. You could also say a backwards time traveling electron traveling west strikes a barrier, which cause it to change direction so that it is now traveling south. Both these explanations are equivalent as far as the math is concerned.