Why do so many Muslim Women Cover their Heads with a Scarf?

The act of covering one's hair by Muslim females is an integral part of the larger concept of Hijab. Hijab, in essence, is the notion of displaying a sense of modesty in dress and demeanour.

Modesty and chastity are very important ideologies in Islam, and the most effective approach to achieve these qualities is by prescribing standards on behavior and the dress of Muslims. As a result, Muslim women who choose to follow the tenets of Islam are asked to cover (or veil) their bodies (all of it, except the face and hands) from men who are not either their direct family members, or their husbands. In this way Muslim women are recognized as individuals, who are admired for their mind and personality, and not for their physical appearence.

For more information about the concept of hijab, especially it's philosophical and practical importance, feel free to read the following online book by the late Ayatollah Murtadha Mutahhari:

http://www.al-islam.org/modestdress/