The crescent moon is supposed to represent the phase of the moon on the night of the first revelation of the Qur'an in 610, and it was a common symbol used on early Islamic war flags. It's kind of an unofficial symbol, as Islam doesn't have a "real" symbol, in the sense that the cross has come to represent Christianity, for example.

The star was added during the Ottoman period (the crescent-and-star was first adopted under Mustafa III in the 18th century), but its provenance is unclear (i.e., why a star, and why with the number of points it has -- which has changed).