In order of importance, imo:
1 - Piracy. The ultimate system seller (same goes for the DS too)
2 - PS2 was THE videogame market back then. PSP was simply created to be the next PS2, now on the go.
3 - Monster Hunter and GTA, the two incredibly important games.
4 - Great support from companies like Capcom, Konami, Level 5, Square...
If you think about it, everything Vita does not have in the moment.