I think it's ships, or something else that requires characters of different classes. There are seven circles above each spot, which corresponds to the number of stars a character can have. I think you plug characters of certain classes (maybe not all in the game yet) into the spots, e.g. a Pilot in the arrow, a Droid in the square, etc. The green plus indicates you have one or more characters of the appropriate class available for that slot. The small squares would show the equipped character's icon.