Silencing is a less harsh way of keeping unpleasant guests at a distance and that can give them a hint - unless there is no use in talking to them and asking them to refrain from their rude behavior.

Go to the Broadcasting page, at the "My Show Controls" tab, you will see the section "Who can chat" and this is where you can choose who is allowed to type in your chatroom and who is sentenced to be silenced among your visitors.

Even though this feature might come in handy, it may also negatively affect traffic in your room, so remember that you also have the option to ban or mute a specific user who's being rude or offensive instead.