A LAN world means if someone is playing Minecraft using the same modem/router as you, they can come into your world and play with you.
Yes with LAN. Just get your friend to open a single player world to LAN and then click on multiplayer and select his world
LAN world
you send a redstone signal to it
If your using the latest version(PC) then hit the Esc/menu key and scroll down to you see something like "Open world to Lan" and click it.when you exit that map or minecraft and reload the world will no longer be in Lan mode.