This BDU belongs to either an AMMO (2WO) Troop or a Weapons Loader (2W1). The missile badge on it is 'awarded' for either supervising those who directly maintain or load missiles, EX AIM 9Ms or AIM 9Xs, or for being a troop who maintains or loads missiles. The star and reef signify different levels of the badge persay.
I wear one myself on my uniform, without the star and reef. Mine is the basic badge, as I'm only a E4 and a 5 level, the star is typically added when the troop gets his 7 level training for his AFSC, and the reef when he gets his 9 level training.