In the heat of summer or the frost of winter, you can tell that a woman is a religious Orthodox Jew by the fact that she covers her hair. There are several reasons Orthodox Jewish women cover their hair. Modesty, or tzniut, is the primary reason: when a woman gets married, her hair has a certain sexual potency to it. You'd think that wasn't the case, especially regarding someone with a bad case of the frizzies. But no, it's true, so a woman's hair should be saved specifically for her husband. A Jewish woman can cover her hair with a hat, a snood, a kerchief (known in Yiddish as a tichel and in Hebrew as a ?????) or even a baseball cap.
Wearing a wig is a widespread practice in the Western world because of the fact that many fervently Orthodox Jewish women are in the workplace and they need to dress the part. However, wig hair is either dead or synthetic, so it doesn't impart the sexual energy that a woman's own natural hair does. And it keeps in line with the second reason that an Orthodox Jewish woman covers her hair: in order to remain at least somewhat separate from outside Western culture.
When a religious Jewish woman puts something on her head, it symbolizes the fact that she is one of G-d's own. G-d commanded the Jewish people to be holy and separate. Unfortunately, Western culture is all about shaking the booty: who has the best body, who is the sexiest, who has the most money, etc. That kind of attitude goes against everything Judaism is supposed to represent. Jewish women cover their hair to proclaim their loyalty to Jewish religion and to her husband.
On one hand, an Orthodox Jewish woman is supposed to take care of herself and to always look as good as she can because she is the daughter of G-d, the King. That makes her a princess (so yes, there is some truth in the derogatory acronym JAP: Jewish American Princess). But on the other hand, royalty has to be separate from the muck. When an Orthodox Jewish women cover their hair, they are saying to the world that the ideology they choose is one of Judaism and Torah vs. materialism and body-centric thought mode, which is an ideology or even a religion all of its own.
And the general rule regarding covering hair is that the more hair that is covered, the better. Many people make fun of the fact that in some Hasidic sects, the women shave their heads. Some people say that that was a practice initiated when the rulers of the host countries would partake in the "right of the first night", that these Jewish women would shave their heads in order to make themselves ugly to these rapists. However, many others say that because of the mystical properties of a Jewish woman's hair, the less hair visible to the outside world equals the more blessing available in the family and home.