A LAN stands for Local Area Network. It is a basic computer network, a simplified version of what you may see at your school, polytechnic or business.
A gaming LAN (AKA LAN party) involves networking computers or gaming consoles together so that players can compete against each other. Examples are networking Xbox360's together in a LAN so that upto 16 players may compete against each other at Halo 3 or Call of Duty.
Further information about LAN's can be found here
Further information about Gaming LAN's can be found here
