Time is certainly a very complex topic in physics, but there is no real doubt among physicists that time does really, truly exist ... they're just divided a bit on what causes this existence.
The Arrow of Time and Entropy
The phrase "the arrow of time" was coined in 1927 by Sir Arthur Eddington and popularized in his 1928 book The Nature of the Physical World. Basically, the arrow of time is the idea that time flows in only one direction, as opposed to dimensions of space which have no preferred orientation. Eddington makes three specific points in regards to the arrow of time:
A. It is vividly recognized by consciousness.
B. It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.
C. It makes no appearance in physical science except in the study of organisation of a number of individuals.
The first two points are certainly interesting, but it's the third point that captures the physics of time's arrow. The distinguishing factor of the arrow of time is that it points in the direction of increasing entropy, per the Second Law of Thermodynamics. Things in our universe decay as a course of natural, time-based processes ,but they do not spontaneously regain order without a lot of work.
There's a deeper level to what Eddington says in point three, however, and that is that "It makes no appearance in physical science except..." What does that mean? Time is all over the place in physics!
While this is certainly true, the curious thing is that the laws of physics are "time reversible" ... which is to say that the laws themselves look as if they would work perfectly well if the universe were played in reverse. From a physics standpoint, there's no real reason why the arrow of time should by necessity be moving forward.
