Answer:
In a non-vertical fault (where the fault plane dips), the footwall is the section of the fault that lies under the fault, while the hanging wall lies over the fault.
The names come about from the mining industry because important ore minerals were commonly deposited along fault planes. In a mine along a fault, the miner would be standing on the block lower block and hanging his lantern from the upper block (hence, foot wall and hanging wall).
In perfectly vertical faults, you cannot designate a footwall or a hanging wall.