The nurse is a funny character in the play who constantly uses the wrong word — with funny consequences. This is called a malapropism, and this line is a good example of one. The normal expression is to say that you "swear by your head that something is true," meaning that if it’s false, they can cut off your head. The nurse, however, swears on her maidenhead, her virginity, which does not mean much, since she became a mother long ago (see line 20).