It basically allows you to mute Kik conversations so you don't receive notifications when someone posts something new.
This option is useful if you want to keep an eye on a conversation or group chat, but if you're doing something important or you don't want to be distracted, then you won't get annoying push notifications.
Kik came up with a clever idea of allowing people 3 different muting options:
Mute a chat for 1 hour
Mute a chat till 8am next morning (useful if you're going to sleep and a group chat is still buzzing).