A MAC address (Media Access Control) is a OSI-Layer 2 48 Bit long unique address. Well at least it should be unique. Each network-device in a computer,- usually this is a network card and a computer could have more than one network devices,- has its own address which is composed from the OUI (the first 24 bits )and a unique ID (the last 24 bits).
Remember! Conmputers not necessarily talk to each other. rather think of network cards can talk to each other.
This address is used by the Switch or a Hub to send data frames over the Ethernet to your computer.
Most people are buying a device which actually is a router and a switch combined. the router is sending and receiving data through networks using ip-addresses. The Switch is sending and receiving frames to network cards using MAC-Addresses.
Because internetworks generally use network addresses to route traffic around the network, there is a need to map network addresses to MAC addresses. When the network layer has determined the destination station's network address, it must forward the information over a physical network using a MAC address. Different protocol suites use different methods to perform this mapping, but the most popular is Address Resolution Protocol (ARP).