In firearms terminology, the receiver is the part of the firearm that houses the operating parts of the gun. In most cases, it is made up of forged or stamped metal, and the moving parts reciprocate and cycle within it.
In strictly legal terms, the receiver is the actual firearm itself, and as such it is the controlled part (without which operating is impossible). Generally, the law views the receiver as that part of a firearm housing that has the serial number upon it. Thus, in the case that a firearm has multiple receivers, the legally controlled one is the one that is serialized.