Time dilation is the effect that for some objects, less time as passed than for others, depending their position and velocity. It is a consequence of relativity.
Special relativity implies time dilation based upon the relative motion of two objects. General relativity also produces time dilation depending upon how curved space is, e.g., due to gravity (gravitational time dilation)
Cosmological time dilation is the apparent time dilation of events viewed from large (high redshift) distances.
Time dilation challenges intuition based upon daily experience, but is not only proven, but some technology, such as GPS, requires it to be taken into account, or it doesn't work.