Mute allows owners and above to ban a user without them knowing. Guests in the chat will not be able to see the ban message, whereas members and above will.
To mute a user, click on their name, click "Ban", and press the "Mute" button. The maximum amount of time that you can mute a user is 1 hour; however, this can be extended with GControl.
Note: You must be an owner to use this power. However, similar to the ban duration, GControl allows you to customize which ranks are allowed to mute.