Hydrocodone is a codeine derivative. Codeine, aside from acting as a pain medication, supresses respiration, thereby acting as a cough supressant. As a result, many cough medications do contain hydrocodone. From what I've heard, Tussionex is one of the most addictive (not sure why).

As for the acetaminophen combination factor, it is partially used for deterring abuse (over 4000 mg of acetaminophen daily causes liver toxicity, which is why drinking alcohol while taking Tylenol is a bad, bad idea). It is also simply used as an addition pain killer to assist the effects of the hydrocodone. Other combinations are also used, such as ibuprofen in meds like Vicoprofen.