This is a summary of everything that's happened within your channels in your teams list. Select Filter at the top right corner of the feed to show specific types of messages such as unread messages, @mentions, replies, and likes.
When a red circle appears next to Activity, you have a notification—such as an @mention or a reply—in your feed. These notifications remain in your feed for 14 days. After that they expire and no longer show in your feed.