This is a new function accessible via the Sidebar (options 3-2) and lists all missions available at the moment. When the Skunk enters a new zone or sector the all available mission will be added to the BBS. The exception are the hidden or secret missions. In order to add them to the BBS they must first be found by flying close to the surface of stations. Mission will stay in the BBS for a limited amount of time or until you go out of range such as when travelling through a Jump Gate.
Please note that if you're loading an existing save after updating to version Rebirth 4.0, you'll need to change zones before the BBS will begin to populate.