What was it for?
While a century of research has finally answered the question what the mechanism did, we are actually no nearer answering the question what was it for. There are numerous suggestions, any of which could be right.
For the ancient Babylonians, predicting eclipses was very important, as they were thought to be bad omens. Indeed the mechanism could be thought of as being a political tool, allowing the ruling authorities to have dominion over their subjects. It has even been proposed that one reason we know so little of these mechanisms, is that they were bound by military or political secrecy.
Another common suggestion is that it could have been an aid to navigation, especially as the ancient inhabitants of Rhodes were notorious for their navigational skills. However this seems unlikely as it would be an impractical device to use at sea, and seems excessive for the purposes of navigation.
It would have been a more useful tool to astronomers, for assisting in making land based astronomical measurements. Indeed, with knowledge of eclipse timings it would assist in making measurements on a world scale, for example longitude.
The first Mechanisms could have been built purely on the basis of seeing if it could be done. Indeed researchers are still making models of the mechanism today, to see if the theory can be put into practice. Unfortunately this does not apply in the case of the Antikythera Mechanism, as it is not thought to be the first of its kind.
A final possibility is that it could have been used as a teaching aid. From the evidence of its construction, it was designed to be taken apart easily. This could be merely to assist in cleaning and servicing the mechanism. However, you only have to observe a model maker showing off his model to an audience, to appreciate what a superb teaching device the mechanism is, as well as being a practical and useful astronomical instrument.