Of course, moon phase indicator is not one of the most useful watch complications; it serves more for an aesthetic pleasure than for a real need.
The appearance of the indicator may varies in different models, but it always shows the Moon as it would be seen from Earth (only one illuminated side is visible from our planet). The indicator usually looks like a rotating disk that shows the progression of a lunar cycle, the duration of which (from new moon to new moon) is 29 days, 12 hours, 44 minutes and 3 seconds. The complication, as it can be understood from its name, shows different moon phases, when it is full, half or quarter. The phases are typically displayed through an aperture on the dial, which shows an actual graphic image of the moon. Just as the moon travels across the sky, the image travels across the dial of the watch.
The indicators themselves looks different, they may have more or less realistic image, and there is no universal location on a watch dial either. Some indicators are extremely accurate, requiring adjustments only each 120 years or so.
As it was told earlier, moon phase indicator nowadays serves a little practical application. Of course, it can be helpful for farmers and fishermen, for which the information about moon phases is important. But to be honest – have you ever seen a farmer who is wearing elegant high-end mechanical watches while out in the field? However, an aesthetically beautiful of this complication makes it a highly desired feature for most watch enthusiasts.