The 'Project Messages' stream shows you all posts that are published by your channels, ordered in a chronological way. Even when you post via a channel itself, such as Instagram, these messages will still be shown in this stream.
Underneath the posts, you can see the number likes, comments, shares and other actions (which depends on the channel the post is posted to).
The same as with the 'All messages' stream, the number next to the 'Project messages' is the total number of posts in the stream.
The meaning of the three icons in the upper right corner of the stream window is explained here.