What does it tell us about Greek Astronomy?

Without a doubt it tells us that both Ancient Greek astronomy and mathematics were very advanced. This has to be placed in perspective as part of Greek astronomy comes after the long scientific tradition of the Babylonians, who built up a remarkable collection of astronomical data and discovered the repetitive patterns in that data. The Greeks placed these data into a new perspective. As an indication of the astronomical knowledge represented by the Mechanism, consider the FAQs regarding the Metonic, Callipic, Saros, and Exeligmos Cycles.