a MAC address is a "Media Access Control" address or something like that.

Basically it's a unique identifier for your network interface (but it's easily spoofed/overridden in software).

MAC Addresses are basically a lower level version of ip addresses, or at least that's an easy way to think of them. They're used in negotiating things like who gets to talk on the wire at what time, and who they're talking to. Pretty essential for ARP (address resolution protocol) to function, letting network nodes know who a given broadcast is addressed to (which is particularly handy on shared-media network hardware, like wireless, and dumb devices like hubs).

Lots of places and people (including most DHCP servers, and many ISPs that use them) consider a MAC address to be a globally unique identifier of your device. And they're usually not wrong about it either (except, again, that MAC addresses can be spoofed and cloned, which comes in handy for most routers).