I guess I missed the most important detail!!! In short, it tracks the phases of the moon over the course of a lunar month, which is approximately 29.5 days.
Jason Heaton does a good job of explaining it in further detail here
favorite passage: "Never a complication of necessity, the moon phase is more about the watchmaker’s connection to time itself. It is a sort of microcosm of the larger gear train of our universe with its intermeshing planetary orbits and cycles."