Advil, or Ibuprofen, binds to an enzyme called cyclooxygenase (COX-1 and COX-2). It blocks the beginning of a pathway (maybe someone else can fill in this part for me) that leads to inflammation. It is a non-steroidal anti inflammatory drug (NSAID).

To begin with we would have to know what headaches are on a mechanistic level and at least when I took a neurophysiology of pain course in grad school the answer was pretty unclear.