ROM is simply Read Only Memory.
Unlike RAM, ROMs cannot be written to. At one point, ROMs are also typically slower than RAM.
ROMs come in several flavors:
PROMs can be programmed ONCE then read many times. If there are any mistakes in the PROM code, the entire chip must be discarded. While PROMs can be read in a normal board, they need to be programmed in a special device (since programming them often requires special voltages).
EPROMs can be erased after they have been programmed. Normally there is a small window in the chip in which exposure to UV light will erase the EPROMs programming. EPROMs also need to be programmed in a special programmer.
EEPROMS can be erased electronically, and re-programmed, usually through the application of higher than normal voltage. In modern EEPROMS this is generated internally. Unlike EPROMs, EEPROMS can be re-written in-circuit.