This symbol is found on many ancient stone carvings, and represents the Goddess Tanit.
Tanit was the Carthaginian and Phoenician Goddess of the moon. Tanit was the Patron of Carthage and the consort of the god Baal. She may have been related to the goddess Astarte/Ishtar.
Bulla amulet depicting Tanit
Tanit on a stele with wands and celestial symbols
This emblem, commonly recognized as the symbol of the Islamic faith, has actually acquired its association to the faith by association, rather than intent.
The star and crescent symbol itself is very ancient, dating back to early Sumerian civilization, where it was associated with the sun God and moon Goddess (one early appearance dates to 2100 BCE), and later, with Goddesses Tanit and even Diana. The symbol remained in near constant use, and was eventually adopted into the battle-standard of the Ottoman Dynasty, who are mainly responsible for its association with Islam. As the Dynasty was also the political head of the faith, it was inevitable that their symbol would be associated with Islam as well. It should be noted that there is no mention of such a symbol in the Koran, the Holy book of Islam, nor is there any relationship between the crescent and star and the Prophet (whose flag was black and white, inscribed Nasr um min Allah, “with the help of Allah.”)
Today, the star and crescent is widely accepted as a symbol of the Islamic faith, and is used in decorative arts, jewelry, and national flags- much like the cross in Christian countries. It is associated with the use of the moon to time festivals. It is, however, not accepted by all Muslims- some Muslims consider it un-Islamic and even blasphemous.
Sumerian star & crescent