Mute is a feature which allows you to silence (or turn off notifications) a conversation that’s not relevant right at this moment. You can choose to mute conversations for an hour, until the next day, week, until all messages are read or until you unmute the conversation. When the mute time period is over, a notification will be triggered to you.
To mute a conversation you need to right-click on it and choose Mute from the drop-down menu that appears - and for what time period you wish to mute the conversation. After that this conversation will be labeled as Muted conversation and you can find the conversations from the Left pane conversation list under the label Muted.