At the end of the game, there's a point where Yuna begins walking through the Farplane (after the final series of fights). If you press X, you'll begin a dialogue with one of the NPC representations of a former Aeon. Simply choose the "Yes" option, and you'll be treated to the scene where they reunite after the end of the other ending videos.

But if you're not going to play the game anymore, you might as well just YouTube the encounter.