Local Area Network, also known as LAN, is a general technical term for computers when they are connected through a small network of computers, like inside a home or a small office.
For Diablo I/Diablo II, it is a type of multiplayers network play where the primary network type is IPX/SPX. Diablo III is confirmed to be launched without LAN support. The only multiplayer gaming mode with the third game in the series is through Battle.net 2.0.