In-app notifications indicate unread messages in conversations you're a part of. When someone sends a message in a group you belong to, or when you receive a direct message, the conversation name on the left sidebar will turn bold. In addition, a red badge will appear to the right of the conversation name indicating the number of unread messages.
Notifications will clear when you enter a conversation and read new messages.
You can also change your notifications settings to turn notifications on or off for individual conversations by muting the conversation.