In most traditions, the greater sabbats are the cross-quarter days and the lesser sabbats are the equinoxes and solstices. To me this doesn't make sense. The equinoxes / solstices are marked by the specific position of the earth and are calculated astronomically. The cross-quarter days cannot be calculated without them. Therefore, I like to think of the equinoxes / solstices as greater sabbats and the cross-quarter days as lesser sabbats. Really, I'm not sure why any of the sabbats would have a greater or lesser significance. The sabbats are: Yule / Winter Solstice, Imbolc, Spring Equinox, Beltane, Summer Solstice, Lammas, Autumn Equinox, and Samhain. The Witch's New Year is commonly celebrated at Samhain (Halloween).
Now you know what the WotY is. The moon has 8 main phases: new moon, waxing crescent, 1st quarter, waxing gibbous, full moon, waning gibbous, 3rd quarter, and waning crescent. If I could superimpose the moon phases over the WotY, Yule would correspond to New Moon. Winter Solstice is the longest night of the year and new moon is when the moon is hidden in the sky. In Egyptian Paganism, winter solstice is the new year. The equinoxes correspond to the 1st and 3rd quarters. The moon is in perfect balance with the light and dark halves; likewise day and night are equal lengths.
Celebrations of the moon are called esbats. In contrast, the sabbats celebrate the sun.