Time dilation is the phenomenon that time seems to slow down in other frames of reference.
The most common calculation of time dilation in introductory physics involves the Lorentz transformation resulting from two reference frames in relative motion to each other. E.g. The observer from one frame of reference, if able to observe a clock in another relatively moving reference frame, will notice that the clock is ticking away slower than the clock in her own reference frame. The rate is determined by the Lorentz transformation. In fact, Lorentz figured out the formula based on mathematical principles alone, but found no practical use for it. It was Einstein that was able to use the formula to calculate time dilation!
Review basic concepts of relative motion and reference frames, as most students have a hard time visualizing the problems associated with time dilation.
Time dilation occurs all the time; however, the effects are negligible for small changes in gravitational strength or speeds not close to the speed of light.