MCPE multiplayer doesn't work

The main menu multiplayer settings are the default and can be changed by a per world basis. You can't change this setting in game. Change it at the world list.

You can't actually change if the game is multiplayer or not while you are playing that world. What you'll have to do, is exit out of the world, click the pencil icon next to it, go down to multiplayer, and then you can select "On/Off"