Remote Play was really underutilized on the PSP, you could really only play PS1 games with it.
What it can do:
Play PS1 games (discs and PSOne Classics)
Listen to music CDs
View/Listen to - music, pics, videos on the HDD
View/Listen to - music, pics, videos via a media server
With the PS4 just out and the Vita already out, we should see a great deal more out of the idea. It can play PS4 games in the same way that the PSP could play PS1 games, which goes to show how radically different the hardware is all around.