If you have a LAN in your house this should be easy, what you do is go onto one of your minecraft worlds and then press Esc to pause it, then you click on Open Lan and then it comes up with a IP adress. After that it should come up on the other computer, if it doesn't then click on Direct Connect in Multiplayer and put in the IP if you can't remember what it is then you go to your computer thats running the Minecraft and in the game press T and it should come up with the chat log and the IP adress should be there then put it in and "VOLA" your in.
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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.
Options > Open to LAN
LAN world
You can play LAN multiplayer in the latest version. You just use the menu option to open the world for LAN connections and send the IP to someone else connected to your LAN.
LAN means Local Area Network. LAN World on Minecraft basically means that anyone else playing from the same router/modem as you can join your world.