I am not sure caffeine affects the phamacokinetics of aspirin. I would assume the combination is useful to have both effects in one pill: pain relieve (more the thousands known and other unknown effects of aspirin) and alertness (from caffeine). Hope it helps.
very often the cause of headaches is a relaxation the blood vessels of the meninges under the influence of some prostaglandins or by adenosine release. Aspirin is a COX inhibitor, and caffeine is a blocker of adenosine receptors. Thus, using a combination of aspirin plus caffeine, we're trying to one shot to kill two birds with one stone.