In special relativity: From the point of view of an observer (more precisely: an inertial observer), a moving clock goes slower than an identically built clock at rest. All other processes moving alongside the clock (for instance: everything happening aboard a rocket speeding by) are slowed down in an identical fashion.
Time dilation can be mutual: When two inertial observers speed past each other, each will find that the other’s clocks go slower.Some aspects of this unfamiliar mutuality are explored in the spotlight topic The dialectic of relativity; a geometric analogy is presented in Time dilation on the road.
In general relativity, there is the phenomenon of gravitational time dilation: Roughly speaking, clocks in the vicinity of a mass or other source of gravity run more slowly than clocks which are farther away. This phenomenon is closely related to the gravitational redshift.