Drawing Down the Moon is a ritual possession that is performed in some Wiccan and modern religious Witchcraft Circles. It is a direct invocation of The Goddess by the (usually) High Priestess. The Goddess enters the Priestess’s body and speaks through her mouth, often delivering blessings and divination.
The term Drawing Down the Moon seems to imply a feminine deity, but some use it regardless of the perceived gender of either deity or vessel. The term Drawing Down the Sun is sometimes used when the deity and/or vessel is perceived to be male.
While a variety of techniques may be used, dancing and chanting is often used to achieve an altered state of consciousness and rhythmic prayers call down the deity into the vessel. The specifics vary by tradition. It is usually done during a private full moon Esbat, where the Goddess is represented by the Moon, and rarely at public gatherings.