They're usually referred to as "cigarette burns" and indicate when the operator is supposed to switch from one reel to the next. From my observation, one shows up, then another, and then the reel is supposed to switch.
In big movie theaters, there's not actually an operator running the movie, the reels are just patched together. At my school movie theater, however, there's a student in charge of switching reels and half the time they mess up and miss the crucial moment, so you can see how important watching for those dots are. Also, if you notice during movies, they usually don't happen in the middle of an important scene, and there's usually a few seconds of "fluff" after the second dot to give the projectionist a little bit of leeway so if they don't switch it over precisely, it's no big deal.