Removable Batteries
The PSP uses a removable battery. Using removable batteries allows you to charge spare batteries while you play. This way you don't have to find a plug when your battery dies, you just replace the battery and resume playing. On the other hand, the PSP's removable battery is proprietary. This means it has been designed specifically for the PSP and will not fit other devices, nor can you use other batteries on your PSP.
Internal Batteries
Both the PSP and the PSPgo have internal batteries; however, there is a difference between their internal batteries. The PSP's internal battery controls the internal clock and other minor memory settings. The internal battery on the PSPgo is the sole battery the system uses. The problem is when your battery dies you have to plug your system in to continue playing, or wait until it has charged again. Internal batteries are not easily changed.
Piracy
The PSP became controversial because of a hacked battery. The battery overrode the PSP's boot software and used its own preloaded system software to allow users to play illegal games.
Piracy Prevention
In an effort to reduce software piracy Sony released the PSPgo. The internal battery it runs on cannot be modified, and by using the internal battery there are no risks of piracy similar to that of the original PSP.