What does it mean to Open to LAN in Minecraft?

Ä°t means open a server inside your Wi-Fi connection and only people connecting your Wi-Fi can connect it server

LAN is where if you had 2 laptops/computers in one room and you connect to the same world on Minecraft. I did this with my brother all the time.

It means you can open your single player world to your LAN (Local Area Network), so people on the same network as you have access to the world.
The local network will literally just be people connected to your internet. So if someone else is in your house using the same Wi-Fi, then they can join.

If you open to LAN, other people will be able to join your Single player Minecraft world, just like a multiplayer server.
This doesn't just mean your friends can join from anywhere, they have to be connected to the same network, not just their internet. You also have no control over who joins, so it's not recommended to do this in a public area or school.

When you click on 'Open to LAN' you are faced with two options;
"Gamemode" and "Cheats"
Gamemode decides what gamemode people will be on upon first entering your world, it won't change the gamemode of everyone already in the world.
Cheats allows commands to be used, so you can manually change your gamemode, spawn in items, teleport players etc…

Once you leave your LAN world (if you are the host) then everyone else is booted out, like on a regular server. Once you re-join it however it will no longer be a LAN world, just a regular single player world like your started with.
You would have to open it to LAN again to allow people to re-join.

^-^ Hope this helps! ^-^