To follow posts in your course discussions, select the post from the left hand menu, then click the star icon below the post, the Follow button.
The star icon fills black to indicate you are now following this post. When you view this post in the left hand panel, the star also shows as filled black. For more information about the various indicators in the navigation pane, review How to join course discussions.
Filter discussion posts
In the discussion All Posts tab, you can lists only the posts that you are following, regardless of the topic that they apply to. Click the filter icon across from All posts by recent activity.