The replies are only partially correct.
A Full Format - AKA Low-Level format - creates the FAT structure on the disk drive. A Quick Format - AKA High-Level format - only works on a disk drive that already has the FAT structure on it. The Quick Format basically cleans up the "first sector" pointers in the FAT, so to the operating system, it looks like a new disk. Almost all hard drives are shipped with a low-level format already performed- maybe as a final QC check, maybe to reduce the confused consumer calls. A full Format can erase data, but it isn't guaranteed to.