Cosmological time dilation (or cosmic time dilation) is the phenomenon that events observed at cosmological distances (i.e., with a significant redshift) appear to take longer than they would if they were nearby. Given the expanding distance between us and the event (Hubble expansion), light takes increasing amounts of time to reach us over the course of the event. The lengthening ratio is (z+1)/z, the same ratio as redshifted wavelengths from the same distance, and the two can be considered the same phenomenon. Some such time dilation would occur from the increase in distance irrespective of relativity (just as a musical performance would sound for a longer time if you are moving away from it), but relativity does affect cosmological time dilation, significantly for very distant objects.
Observation of distant events such as supernova light curves do last longer than corresponding nearer events, in proportion to the redshift(s) determined from recognizable spectral lines.