MAC addresses are unique codes that is assigned by the manufacturer to any device that can be connected to a network. Devices require network interface cards to connect to a network (NIC); these NICs contain the MAC address.
MAC addresses contain 6 or 7 pairs of hexadecimal numbers (eg 1A:2B:3C:4D:5E:6F:70) which means there are trillions of possible sequences. The first 5 digits identify the manufacturer of the device.
To secure a network you could specify the MAC addresses of the devices that you would like to be able to access the network.
Side note: if a criminal was using a public network to commit a crime, the router would have recorded his MAC address so they may be easier to track down.