If something is baffling, it's completely confusing or mysterious. You might find your friend's hatred for the taste of chocolate utterly baffling.
A good mystery novel begins with a baffling crime — one that seems at first nearly impossible to solve. You might also find your math homework baffling or wander around the baffling snarl of streets in a city with no idea where you are. The earliest meaning of baffling was nautical, describing winds blowing in all directions. It comes from the verb baffle, which first meant "to disgrace" before it came to mean "to confuse."