I did not know that yesterday!

According to a list of Frequently Asked Questions originally created for the Usenet newsgroup rec.arts.movies, those dots are cue marks that let the projectionist know that it's time to change reels. Film reels generally range in length from 20 to 22 minutes, so there are several "changeovers" in a feature-length film.

Each reel of film actually has two sets of cue marks. Before one reel ends, the projectionist loads the next reel in a second projector, with about nine feet of leader, or blank film, between the lens and the start of the reel. The first sequence of dots, which starts about nine seconds before the end of the reel, cues the projectionist to start the second projector running.

At the second set of dots, which marks the end of the reel, the projectionist throws a switch that changes the sound and picture source from the first projector to the second. At this point, which is usually a dark scene change, the two projectors are cued up at the same point in the film. It's a process that's worked for 100 years,
but the advent of digital projection technology means it's not likely to make it another 100.