Time dilation is a temporal effect on matter moving at speeds near lightspeed. When matter reaches this 'relativistic speed', time dilation becomes apparent. Albert Einstein first postulated time dilation as a side-effect of an absolute lightspeed. In order for the speed of light to remain constant no matter how fast the observer is travelling, time must slow down proportionately for said observer. Thus, the effect produced is a perceived slowing of time for any matter moving at relativistic speeds, from the perspective of a stationary observer, and a perceived speeding up of time for any stationary matter, from the perspective of a relativistic observer.
Time dilation is an exponential effect, which means that it remains small for most of sublight speed, but becomes powerful very quickly when close to lightspeed. If one were ever to reach lightspeed, time would come to a standstill for them (to us), while everyone else would freeze (to them). Time dilation has been experimentally proven several times. By synchronizing two atomic clocks, then flying one for extended amounts of time in an airplane and comparing its time reading with the stationary clock, scientists have discovered a dilation of a few millionths of a second for the airborne clock. Don't think that you'll age any slower by flying, though: if one spent his or her entire life on a non-stop airplane flight, they would only be one-ten thousandth of one second younger than anyone grounded for the same amount of time.