An EEPROM is an electrically eraseble programmable ROM. It is a ROM chip (meaning it will keep its information when you power off the computer) which you can erase without additional hardware (unlike regular EPROMs). It is often used to contain firmware, such as the BIOS in a desktop.
From http://en.wikipedia.org/wiki/BIOS: BIOS software is stored on a non-volatile ROM chip on the motherboard. ... In modern computer systems, the BIOS contents are stored on a flash memory chip ...