I have been asked what the different gatherings of the coven are for so here is a detailed explanation of the different type including full moon, new moon, and Esbats and Sabbats.
During the year witches celebrate the Wheel of the Year, it includes the 8 Major Sabbats. Those Sabbats are Samhain, Yule, Imbolc, Ostara, Beltane, Litha, Lammas, and Mabon. These are the solstices and equinoxes, known as the quarter days, and the mid points. Yule and Litha are both solstices, and Mabon and Ostara are the equinoxes. Samhain is the pagan New Year. Imbolc, Beltane, and Lammas are the other three cross quarter days. Samhain, Imbolc, Beltane, and Lammas are what is known as Fire Festivals, and they are usually celebrated with bonfires. Usually we celebrate these holidays with a feast and rituals. In the southern hemisphere these holidays are reversed in date from what we celebrate in the northern hemisphere. It is customary that the entire coven attend these events. Even though they are held open circle we're all there!
As well as the 8 major Sabbats, we also celebrate what we call Esbats. These are gatherings held for different purposes and usually are scheduled around lunar cycles. These gatherings are held bi-monthly to discuss and plan upcoming Sabbats and the coven workings. It is an opportunity to preform special rituals (fertility, luck, healing, health, etc) and also a time to schedule training of new initiates and students along the path. The most common time to hold these gatherings is during the new and full moons but that's not set into stone. Usually they are worked around schedules and held to fit a frame when others can attend.
Full and New Moon Esbats
Gatherings are held during the full moon each month to allow closer workings to the Goddess. As the moon waxes and wanes so does magical forces. During the time the moon is getting fuller, or waxing is a time for drawing things to you, such as knowledge. This is why most tutorial gatherings are held during the new moon. The waxing moon can have positive influence over things you wish to gain. The waning moon is a great time to hold a banishing ritual and to get rid of unwanted things. All full moon rituals are held at night because full moon rituals are held to work with the Goddess and the moon is her symbol. The time of the dark moon is a time when one can clear their minds of unwanted and negative energies.
I hope this helps to explain why we celebrate gatherings and feasts when we do.