Crescent Moons generally represent birth cycles and fertility. As you can imagine, the moon means a great deal to a wide variety of cultures and its symbolism can vary quite significantly.
In Wicca, the moon is sometimes associated with Demeter, Persephone and Hecate, also known as The Mother, the Maiden and the Crone who represent a life cycle in their changing phases, which is quite relatable to the phases of the moon.
The word “crescent” comes from the Latin term "ceres" meaning to “bring forth, create” and "crescere", the Latin term for “grow, thrive”.
In many cultures, its seen that the crescent moon represents new beginnings, life and death, which makes this symbol popular amongst many religions.
In Native American lore, it is said that the cresent / new moon is a time to let things go, whereas the full moon is the time for new beginnings. The thinking behind this is that during the nights of a crescent moon, there is less light than that of a full moon, and hides the emotions you display, while during the full moon, your aspirations and hopes are transparent and visible.
The crescent moon is also separated by their phase in the cycle. The waning crescent and waxing crescent.
Waning Crescent: symbolizes the expulsion of negative energy in your life, getting rid of things you know you don’t need, or those things/people/habits, etc which are harming you.
Waxing Crescent: symbolizes growth and creativity. Real general there, but it carries a broad spectrum. Use your imagination.