The triple moon is a Goddess symbol that represents the Maiden, Mother, and Crone as the waxing, full, and waning moon. It is also associated with feminine energy, mystery and psychic abilities.
The Maiden represents enchantment, inception, expansion, the female principle, the promise of new beginnings, youth, excitement, and a carefree erotic aura. The Maiden in Greek Mythology is Persephone - purity - and a representation of new beginnings.
The Mother represents ripeness, fertility, fulfillment, stability, and power. The Mother Goddess in Greek mythology is Demeter, representing wellspring of life, giving and compassionate.
The Crone represents wisdom, repose, and compassion. The Crone in Greek mythology is Hecate - wise, knowing, a culmination of a lifetime of experience.
These aspects may also represent the cycle of birth, life and death (and rebirth). Neopagans believe that this goddess is the personification of all women everywhere.