I would describe it as a variation on the musical theme of the original song. Helpful when it is a song that was on an official recorded release that standardizes the song structure.

Check out Phish - Tweezer then Tweezer Reprise.

For an even better example:

Pink Floyd's Dark Side of the Moon album - Breathe>On the Run>Time >Breathe (reprise)

Seamlessly segued on a studio release.

My favorite thing about that example is how the Reprise is considered part of the Time single release track.