I am a Modern Orthodox Jew. This is a huge part of who I am and does effect a lot of what I wear and what I do. Through various biblical reference we learn that a married woman should cover her hair. When and how much are questions that people more learned than I have been struggling with for a very long time, but the base fact, that according to traditional Judaism married women wear something on their heads is not really arguable.
From a modesty point of view it is something that becomes private. One of the parts of us that are designated for our husbands. Just as we teach children that "what is under a bathing suit is yours and yours alone, so to does our hair take on this status when we get married. (Why our hair and not, say, our nose or our pinky? I have no idea.) In essence, we cover our hair as a sign both to ourselves and those around us that we are married, and therefore unavailable. In the religious world it is as common a sign of being married as a wedding ring is to the rest of society (Although thankfully for jewelers like myself we also have wedding rings!)
There are a number of ideas of how this should happen. The more traditional streams of Judaism say that it all must be covered all of the time and often use wigs, snoods, scarves etc, that will cover every last strand of hair at all times. Many even sleep in thair coverings of choice. Less traditional streams believe that you should wear a hat or other headcovering for religious rituals (prayer, ceremonies, etc. Along the ideas of wearing a hat connotes respect).
There are also those who have chosen to leave this idea behind all together.
And in case you wondered (and this has nothing to do with the post referenced above except the Jewish tradition, and the fact that she references this movie herself in her entry, which reminded me that I'd taken this quiz once) ...
Take the Fiddler on the Roof quiz at ChaiSpace.com