The main reason for wearing Jilbabs (also knows as Abayas in the Middle Eastern countries) as a Muslim woman is that it is a commandment of Allah (God) as can be seen by the following verse from the Quran:
"O Prophet (May Allah's peace and blessings be upon him)! Tell thy wives and thy daughters and the women of the believers to draw over them their cloaks (veils). That in the least so that they be recognised and not be molested." (Surah Ahzaab, Verse 59).
Islam is a way of life for the Muslim man or woman, they are supposed to follow the commandment of Allah, Muslims believe the Prophet Muhammad (Peace be upon him) was an example to mankind and that they are should follow the way shown by him, this is everything from how to sleep, how to eat, what to wear, how to get married and everything else that a person needs to know to live a healthy and fulfilling life as a Muslim.
There are many different sects within Islam, who all interpret Islam differently according to their understanding of the Quran and Jilbab (the sayings and actions of the prophet Muhammad). This has led to some Muslims appearing more Islamic than others. The toughest stance by Muslim scholars for women's dress, is for the whole body to be covered with loose clothing and the face covered with a Niqab and even the eyes should be covered with a veil. The softest stance is for a Muslim woman to wear a loose Jilbab or clothing with a headscarf.
The way a Muslim woman is identified is by her wearing the Jilbab and Hijab (a headscarf), whilst other Muslim women may choose not to wear Islamic clothing but are practicing Islam as they deem practical or suitable to them, which according to Islam is very sinful. This can be seen by the following saying of the Prophet Muhammad (peace be upon him):
"Many women are clothed but naked in reality. Such women will never enter paradise nor will they smell its fragrance."
Wearing a Jilbab or Abaya isn't easy for a Muslim woman, especially in the West due to the stares and verbal abuse that they sometimes have to suffer. It is also hard for those women who decide to start practicing Islam and start wearing the Jilbab, whilst the rest of their family wear western clothing, as they are usually ridiculed or even asked not wear such clothing that some class as backwards.