This tab represents the current user's contact list, i.e. a list of users they communicate with. Having a user in the contact list makes it easier to select the user as a recipient when creating a new message.
The Add users button opens a pop-up dialog where you can select users to be added to the list. The Remove selected button removes users selected by the check-boxes from the list.
Detailed information about the Messaging module can be found in Developer's Guide -> Modules -> Messaging.