Modesty is a fundamental concept in Judaism for both men and women. The Torah considers a married woman's hair to be an intimate part of her body just like other parts of the body which are usually kept covered. According to Jewish law, once a woman gets married, her hair may now be seen only by her husband.
For thousands of years, married Jewish women covered their hair with cloth coverings. Covering hair was never disputed because in the general society, Jewish and Gentile alike, it was considered immodest for women to walk around with their hair uncovered.
When a woman covers her hair with a modest headcovering, she is sending a message that she is modest. A woman who is modest is saying that her body is not to be flaunted to everyone. An interesting phenomena happens when a woman covers her hair in a modest way - she now will be more conscious of the modesty of her clothing and of her behavior. This brings about much dignity and respect, not only within herself, but also to all those who see her.
For many women, covering the hair is a daily reminder of their connection and private relationship with G-d. It is a statement of her commitment to G-d and her commitment to her husband.
We recommend reading this article by Rabbi Zamir Cohen: http://www.hidabrut.com/article/171301/A-Royal-Crown---The-Head-Covering-of-a-Woman