The hilal (Star and Crescent moon) does not, in fact represent Islam. It pre-dates Islam by about 2000 years. It appears, for instance, on the seals and decorations of the Moabites, of Israel, at about 1500BC.

In the past, it was most notably used on the flag of the Ottoman Empire - especially its navy:



So, it became emblematic of Islamic power, throughout Europe and beyond, in this period. It remains the symbol on the national flag of Turkey, for this reason.

From this, many other, largely Islamic, countries (especially many of the ones set up in the dissolution of the USSR) included the hilal in their national flags - in the same way that many European nations include the cross. It's sort-of-cultural, but not very significant. Some suggest it represents the lunar month, the period of fasting observed during Ramadan, but if does, the fact that its existence was common place throughout Arabia and across Moghul India, long before Islam, indicates that is an adoption, rather than central to that faith.

Since the 1960s, various Islamist movements have also adopted the hilal (probably because of its Ottoman connotations), and so it is often assumed to be an inherently Islamic symbol.

It is possible that there is confusion over the way its name sounds similar to 'Halal' (lawful), that many Westerners think it is in some way bound up in Islam itself.