In the Wiccan tradition...
Because the moon's energy is feminine in quality, the Goddess is often symbolized by the phases of the moon. Each phase vibrates on a different level and corresponds to a specific aspect of the Goddess as well as to a myriad of magickal purposes.
The Waxing Moon correlates to the Light Maiden - As the moon grows from light to full, casters following the Wiccan and other traditions utilize this energy for anything that requires growth, increase, or enhancement.
The Full Moon correlates to the Mother - When the moon reaches this stage, it is at its most potent power. This time can be used for almost any magickal working but is especially useful in complex situations and rituals.
Waning Moon correlates to the Dark Maiden - When the moon shrinks from full to dark, casters utilize its energies to work magick on anything that we wish to eliminate or diminish.
Dark Moon correlates to the Crone - While some practitioners use this moon to rest, regenerate, and recoop, most utilize these energies for psychic work, divination, and devling into the past.