To start, LAN stands for local area network. A LAN party is an event where a bunch of gamers get together and bring their computers to one location and play network PC games. The types of games that are played are typically first-person shooters and can also be played over the Internet. The reason someone would haul their computer to another location to play the same games they could play at home is the real interaction. When someone is at home and they frag that sniper that has been killing them for the last 20 minutes, they might say to themselves, "Yes!" When you are at a LAN party, you can jump up and do a victory dance right in front of the little bugger until he cries.
A LAN party is also a great way to meet people in your area with the same interests as you. When you play online, you might be lucky to be in with another person in the same state. Not only do you get to play with local gamers, you will have better speed then ever before. A LAN network can have speeds that are 100 times faster than even a broadband Internet connection.