The receiver is the part of the firearm that houses the operating parts (the fire control group (including the trigger, the magazine housing, the bolt carrier group, etc)). It is most often made of steel (generally stamped, though milled and forged is not uncommon); however, some firearms use forged or billet aluminum alloys, and still others (most often pistols) use strong polymer blends.
Some weapons (the AR-15, FN FAL, etc.) have a "lower receiver" and an "upper receiver"; in this case, the lower receiver usually houses the trigger group, fire control group, and the magazine housing; the upper receiver houses the bolt carrier group.
Submachine guns usually come with a "round section" receiver and "square section" receivers.
On semi-automatic pistols, the receiver is often known as the "frame".