http://www.calo-hacks.com/3.50downgrader.htmlDownload the file here and read the README for full instructions, I believe you boot up Lumines and then the downgrader activates from there I think. You need the right copy of Lumines though, unfortunately they are going at a pretty high price online and Sony has released patched ones onto the market as well.
With the custom firmware you can:
1. Emulate a whole bunch of systems as Tony mentioned, the big one being the official PSX emulator (FFVII, IX, Persona: Revelations, run at full speed). I dunno much about PAL PSX games compatibility, some converters apply fixes but I'm not sure how effective they are. You might have to download NTSC versions of your games to play them...
2. Someone just released a working program that let's you watch Youtube videos on the PSP.
3. Take screenshots and listen to music while playing your Games
4. You can set the processor speed to 333mhz for all games to improve loading times and frame rates.
5. Full brightness is unlocked, you don't need to plug the PSP into an outlet to use it.
6. PDF, txt reader
7. ISO loader, rip your own games and play it from the memory stick, it saves a lot of battery power and loads games a lot faster then UMD Drive
8. Homebrew games and applications (Someone made a Geometry Wars port for the PSP, a Paper Mario styled remake of the 1st level of the 1st Mario game, better picture viewer, etc.)