When the moon cannot be seen and is in the dark phase, this is referred to as the Dark Moon in Old World Witchcraft. Modern astronomers and astrologers call this darkness the New Moon, because the cycle of the moon is about to restart.
Old World Witches are not the only ones who follow this Dark Moon terminology. Several ancient cultures (such as Islam) define this period as the end of the month and the very first crescent of the moon (Witch's New Moon) as the beginning of the month.
The Dark Moon is a night of stillness, contemplation and banishment. The only types of rituals that should be done on the Dark Moon is banishment work or curses/hexes. The Dark Moon is also ideal for all types of divination, as well as working with the departed. The moon is energetically at its lowest point, and is is more conducive to the mentioned rituals.
View Dark Moon Rituals here.
Learn more about Old World Moon Phases here.