What does a wiccan and half moon symbolize?

Since prehistoric times the phases of the Moon have been associated with the fertility periods in a woman's life. It doesn't hurt that the female estrus cycle is approximately the same as the lunar synodic cycle.

A waxing Moon (the crescent that looks like a "D" - without the straight part - and increases ["waxes'] towards full) represents the Maiden, or female who has not yet started her menses (cannot bear children); the Full Moon is the Mother and the waning or declining Moon (looks like a "C") stands for the Crone, the woman who is past childbearing and is now looked to for guidance and wisdom.

Sometimes all three Moons are displayed together and this is associated with Hecate, the Triple Goddess.

Sometimes, of course, the author of the display is only marginally informed and many have come to think of the crescent Moon as just meaning "women" (in the Days of the Outhouse, the ventilation hole in the door was often in a crescent for the Ladies and a pentagram (five-pointed star) for the Gents).