What is Time?
Time is a fundamental element of our everyday existence, and yet understanding it beyond the movement of the hands on a clock is the source of much intellectual consternation. We can start with a classical definition of time - that periodic events serve as a measure of elapsed time. This does not necessarily imply that time is itself a thing or event - rather it is an intellectual perception of the spacing of periodic events. In this sense it is an abstract notion. This perception can then be applied to define other physical quantities, such as the velocity of objects (length/time), acceleration (length/ time2), etc.
With the advent of relativity, the definition of time becomes more complex. Time becomes a function of the velocity of the observer. This creates a circular argument to the first definition, since velocity is a function of time, which is a function of velocity.
In relativity, although the observability of events is an absolute, the simultaneity of two events in not an absolute - simultaneity becomes a function of the perspective of the observer. There can be no absolute time in Einstein's relativity.
This then creates a problem - if time is relative, then every event (past present, future) must co-exist. In our original definition (Presentism) , only the present actually exists. The past is gone and the future has not yet happened. For relativity, all points in time and space must co-exist eternally (Eternalism). The future is already written, the past endures. Reality is like the frames of a movie real - we simply move through time from one to the next. If this were to be true, then time travel would be theoretically possible.
The ultimate irony of this viewpoint is that, only a few years after Einstein declared that a medium of space, the ether, was "superfluous", he had to re-introduce a new theory of a medium of space to be consistent with Eternalism. This new medium of space was curved spacetime; it could not be abstract space since it holds all the information of reality, past, present and future, coexisting forever. Not only must it be a "thing", it must be "everything" - it would be literally the body of 4-dimensional reality. The metric of spacetime must exist even in the absence of matter. To quote Einstein "there can be no space nor any part of space without gravitational potentials, for these confer upon space its metrical qualities, without which it cannot be imagined at all”. 
Relativity was rapidly accepted because of the desperation of the time - the inability of contemporary scientists to detect a medium of space made someone capable of "slaying the beast" quite attractive - it provided an easy exit from an intellectual quandary. But in doing so, Einstein created an even more ungainly monster - the medium of space-time - far more complicated and paradoxical; equally undetectable.