The MAC address is a unique code for every networking device - for example a network card or wireless network adaptor. It's particular to that specific piece of hardware, irrespective of the network to which it is currently connected. The wireless key, by contrast, is a sort of "password" that you specify for your network.
Assuming that you use encryption on your wireless network, every computer that connects to it needs to have the key specified in its set-up.
In addition, you can set up the wireless router to allow only specified MAC addresses (i.e. devices) to connect. This gives you belt and braces security - though nothing is completely secure.