The term Mrs. degree is a derogatory term applied to women who are attending college (usually at the bidding of their wealthy and controlling parents) not to develop a career but primarily to meet potential husbands with high social standing, earning potential, and a college degree. It's usually used like "Oh, she is just here to get her Mrs. degree", the reason being that when she marries her well to do boyfriend her entire identity is going to be consumed and she will become Mrs. Soandso.
Jurph points out (correctly) that people usually spell it out (like M R S degree) so it sounds like the abreviations of other more standard degrees.
Now that the trend in middle class families is to have both partners working this is probably a less common situation. There was a time however when it was fairly normal for parents with money to send their daughters to college with the expectation that they'd finish with some unimportant degree and marry an up and coming doctor or lawyer or somebody like that when they graduated.
These people are looked down upon because they are not taking control of their own lives, and are instead setting themselves up to be the next generation of bland suburban housewives rather than the next generation of thinkers.