Custom Firmware
The firmware installed on the Sony PSP console accomplishes all of the functions that the system can do. However, there's not a huge range of customization. This is one of many reasons that users hack the console and install a custom firmware. Custom firmware also allows use of emulators, cheat engines, "homebrew" games and other programs that otherwise wouldn't be compatible with the standard PSP setup.
Emulators and Homebrew Games
There are a huge number of games that came out for the PSP, some on other Sony consoles, others from different companies. Some programmers also like to work on their own games, for which there are neither publishers nor distributors available -- these are called "homebrew" games. A PSP with custom firmware can be made to play these games.
Cheat Engines
Custom firmware also has the ability to alter how your games work, letting you hack the games. Installing a cheat engine, or a specific game cheat will let you do things the game normally doesn't let you do. For example, a racing game might let you fly, or you could install new cars into the game.
Custom Faceplates
Modifications are sometimes to the software, but many are also on the exterior of the device. You can install a new faceplate that's more interesting than the one it comes with. If you can find a faceplate from another PSP, or a custom-made one, such as a transparent faceplate could be added.
LEDs
The shoulder buttons on the PSP console are transparent, which gives you the opportunity to add LEDs so the shoulders light up. At least one modder has added a sound-reactive chip to the setup, so his LED shoulder buttons light up when the PSP makes a noise. If you have a transparent faceplate, you can also add LEDs to make the faceplate light up when in use.