ROM, PROM or EPROM are used to store information which must be retained when the power is off, typically they would be used to store the BIOS code.
ROM and PROM are memory types which cannot be erased by electrical signals (provided they are not sufficient to damage it!).
The difference between them is:
ROM is normally 'mask programmed' during manufacture. The data is part of the photographic image used to make the IC.
PROM is an empty memory which can be electrically programmed once only, it has no erase function. They allow latest software version to be programmed permanently.
EPROM can be erased and reprogrammed - for example when upgrading a BIOS.
EEPROM is quite different, it is a memory which is designed to be reprogrammed more frequenty, for example the BIOS configuration settings. It can be treated almost like RAM except it retains its contents when power is removed.
Most computers will use one of ROM, PROM or EPROM but probably not all of them.
Brian.