A MAC address is a unique number that identifies a particular piece of networking hardware. You are most likely to encounter MAC addresses in Ethernet networking. Every Ethernet card (wired or wireless) has its own 48-bit MAC address, usually written as 00:20:AF:93:E3:69.
Knowledge of your MAC address(es) are most likely to be needed when doing wireless networking or DHCP, or both. In both cases, the MAC address is often used to identify a particular piece of hardware to the network, and is used as a crude form of access control. (Note that it is not very effective – most modern Ethernet cards can change their MAC address).
MAC addresses must be unique on a network. If two machines with the same MAC address exist on the same network, Bad Things will happen.