What does it do?
The mechanism has 3 main dials, one on the front, and two on the back.
The front dial is marked with the divisions of the Egyptian calendar, or the Sothic year. Inside this there is a second dial marked with the Greek signs of the Zodiac. This second dial is moveable dial so that it can be adjusted to compensate for leap years.
The front dial probably carried three hands, one showing the date, and two others showing the positions of the Sun and the Moon. The Moon indicator is ingeniously adjusted to show the fist anomaly of the Moon's orbit. It is reasonable to suppose the Sun indicator had a similar adjustment. The front dial also includes a second mechanism with a spherical model of the Moon that displays its phase.
There is reference in the inscriptions for the planets Mars and Venus, and it would have certainly been within the capabilities of the maker of this mechanism to include gearing to show their positions. There is some speculation that the mechanism may have had indicators for the 5 planets known to the Greeks.
Finally the front dial includes a parapegma used to mark the rising and setting of specific stars. Each star is thought to be identified by Greek characters which cross references details inscribed on the mechanism.
The upper back dial, is in the form of a spiral, with 47 divisions per turn, displaying the 235 months of the 19 year Metonic cycle. This dial contains a smaller subsidiary dial which displays the 76 year Callippic cycle. (There are 4 Metonic cycles, within 1 Callippic cycle.) Both of these cycles are important in fixing calendars. The lower back dial is also in the form of a spiral, with 223 divisions showing the Saros eclipse cycle. It also has a smaller subsidiary dial which displays the 54 year Exeligmos cycle. (There are 3 Saros cycles, within 1 Exeligmos cycle.)