The Body Control Module is a computer which controls many things in your car not directly related to the engine. Instead of large wiring looms circuits all over the car all the buttons connect to a single computer which in turn turns on the headlights, open the windows, control the central door locking, etc. =A good example is the VAGCOM system in Volkswagens and Audi's.= see comment)
A Body Control Module is almost always specifically programmed to work with a specific car. For example, a BCM of another vehicle will not open the doors when you use your key or remote. Also, when you try to start the engine it checks the number of the key and a number in the Engine Control Unit as a anti-theft mechanism. Your ECU also does this check, but your BCM can do additional checks like locking the doors to prevent the thief from leaving.