Maddening things are extremely irritating: they make you mad. Some drivers have the maddening habit of following other cars too closely on the highway.
If something annoys you a lot, it's maddening. You might try to ignore the maddening tune your sister keeps whistling, or decide to leave a movie half way through because of the maddening acting style of its leading man. The adjective maddening comes from the less-common verb madden, "annoy someone," or "drive someone insane." Both words are rooted in the Old English gemædde, "out of one's mind."