Relativistic time essentially describes time as part of the space-time fabric, something that is determined by the events of space-time, not visa versa, and requires time to be defined when put in relation to an observer or other event. Time in this model is a measurement of at least two simultaneous events. As Einstein put it, paraphrased: In relativistic time what we see is multiple events with different time epochs all occurring relative to the location and speed of some observer. So, in general: Time it is generally thought to be relative to place, speed, and curvature of space. One consequence is that time has been measured to function slower the closer to the light speed one is moving, relative to an observer moving much slower. Also a consequence, no material can travel faster than the velocity of light.
One apparent oddness that occurs due to time being relative, is the phenomenon, "time dilation." This can best be explained by referring right to observed data: Mu-mesons, particles produced in cosmic ray showers, exist on average for 2 microseconds, relative to an observer traveling with them. These particles exist roughly 10 kilometers above the surface of the Earth, and so Mu-mesons that have been observed in experiment on the surface of the Earth must have travelled the 10 kilometers; however, they only exist for 2 microseconds and in that duration of time they could only travel less than a kilometer even at the speed of light, however, also a rule in relativity, all material particles travel at less than the speed of light; how could they travel the 10 kilometers? It turns out that with their increased speed their clocks have "slowed down," significantly, relative to us observers moving relatively astonishingly slowly. Thus no laws of relativity were broken.
Relativistic time is contrasted against the Newtonian theory of an absolute time, a time that carries on at the same rate consistently everywhere in the universe regardless of any events that may be taking place or the speed of those events. Newtonian time is rigidly uniform and linear. Currently, however, most experiment has indicated that time is indeed relative to the simultaneous events that are measuring it.