Locked Movement Control is an option that allows you to lock the place where the joystick shows up on the game.
The joystick that controls the movement of your Brawler always shows up where you touch the screen with your thumb, however, without the "lock movement control" enabled, the joystick still moves around the screen while you control your Brawler.
With the option enabled, the joystick remains fixed on the same place until you release.
This option affects only the movement control joystick. The attack control always show up where you touch the screen and remains locked on the same position while you aim.
To change this preference you must go to the setting page and look the option "Locked Movement Control", next to the language selection.