From Academic Kids
A crescent is the shape you get if you cut out of a circle another circle of roughly the same size, but offset to one side. You might also describe it as the shape the lit side of a sphere takes on if, in respect to the viewer, the light source is behind and to one side of the sphere (as in a crescent moon).
The word Crescent appears in the name of some places:Byzantine Empire. After the Fall of Constantinople in 1453 it was taken as a symbol by the Ottoman Empire. The crescent is now often used to symbolize the Islamic faith. However, it should be noted that the crescent was not a symbol used for Islam by Muhammad or any other early Muslim rulers, as the Islam is, in fact, against appointing "Holy Symbols". Despite that fact many islamic nations and charities use the symbol on their flags or logos (e.g. Pakistan, The Red Crescent.) In this manner it could be argued that its modern usage is meant to signify identity and for devout muslims brotherhood.
Many Christian fundamentalists such as Jack Chick use this symbolism to make a claim that Allah was in fact a moon-god worshipped by the pre-Islamic Arabs. This argument is sometimes used to argue that the god of Islam is different from that of the Jews or Christians.