From Sega Retro
ROM stands for "Read Only Memory". Memory hardware that allows fast access to permanently stored data but prevents addition to or modification of the data. ROMs come in many forms, two of the most commonly used are Cartridges and Compact Disks. Most Sonic games have been released as a ROM. After ROM data has been dumped into a file, it can be modified.
The legality of using ROM dumps of commercial games is in constant debate. Some say that they can be used as "backups", meaning that one can download a ROM of a game they already own in cartridge form. However, copyright laws don't necessarily protect backup sites, so "backup roms" are really only fair in principal, not in law.