When you unfasten something, you loosen or open it. You should wait to unfasten your seatbelt until the car has completely stopped.
To fasten is to hook, close, or latch something, and to unfasten it is to undo it. You might unfasten your dog's leash so she can run free on the beach or unfasten the snaps and buttons on your jacket so you can take it off. You can also unfasten your ponytail, letting your hair down, or unfasten the latch on a gate. The Old English root word is fæstnian, "make fast or firm."