You can think of this box as a cork board where short messages can be left. On your own profile, you will see (and be able to delete) comments left by other users; on another user's profile, you can leave them a comment in this box.

On your own profile, you can see the latest comments left by others. If you wish to delete a comment, just click the relevant “Delete comment” icon:

On another user's profile you can view comment left for them as well as add your own, by clicking the “Add comment” link and filling out the fields in the box that pops up: