The Meaning of Life, the Universe, and Everything.
a LAN world is a world that people can join in your house.... it's kind of like system link on a console game but LAN means Local Area Network or something like that and when you set it up people on your network can join your game
This is basically repeating what everyone is saying but it's simply other people in your network (or house =P) join your singleplayer worlds. If you click "Open to LAN" in your singleplayer world it will come up with an IP. Nobody needs to know that. If you go to mutliplayer it should show up with the Singleplayer world's name and no bars.
If you were wondering, LAN is an acronym for Local Area Network. So if people are in your house/network, they are in your local area.