Formally called Kodak/MPAA Coded Anti-Piracy Code, this was a system developed in 1982 at Kodak labs to trace the theatre of origin of camcorder copies.
It consists of a pattern of small reddish-brown dots that are overlayed on a short series of frames in a movie. Slight differences in pattern and placement are used to uniquely identify a movie print, and thence which theatre a bootleg copy came from.
In theory, these dots are supposed to be virtually undetectable to the "average" movie-goer. Recently, there has been a trend to make these markings more visible so that they withstand video compression techniques, and still allow (for example) DivX copies found online to be traced. In particular, the markings are being more frequently overlayed on white, for greater contrast.
The first wave of popular movies to use this latest technique includes:
Note that these are very different from cigarette burns, which are cue markers for reel changes, as popularly described in the movie Fight Club.