Guessing it's a six sided shaft that fits in a hex bit driver, the swoop at the right end is for a detent so it doesn't fall out. The square end I think you've got figured out already.
Special oversize quick release impact socket uses those. I have one from Apex and have seen them from snap on. QR314 from apex. Think they have them in different size drives, which would justify having a 3/8 and 1/2 drive bits to insert.