By messing with adenosine receptors caffeine reduces one of the mechanisms behind 'sleepiness', that is, the sleepiness you get from having been awake too much.

Because caffeine also has general stimulant effects, particularly at large doses it can also produce the seemingly paradoxical effects that stimulants have on some people. Sure, take enough caffeine and amphetamine and you can stay up and remain approximately functional. But sometimes taking stimulants makes people tired. For example, if I drink a red bull and take a couple of Ritalin tablets I can either fall straight to sleep or stay up for another 36 hours, depending on whether there is task that latches on to the ensuing over-focused attention control systems and overrides the sleepiness impulse.

(Thus goes the typical explanation that I hear from various sources. I take it with a grain of salt. I trust the actual results of experiments somewhat more than the stories that get told in the accompanying discussion.)