Man, with no size relationship whatsover to go on it makes guessing the application that much more difficult. As an example going from that pic I cannot tell how deep the socket is, nor can I truly get a clue as to the OD of the socket, the only thing to compare with is the driver hole in the center of the socket, meaning that unless you have encountered the fastener in question you are pissin up a rope!
I am going to guess that the socket is used for securing the radio antenea mast nut to the top of the fender on older cars.