A maiden name is the name that a woman is given by her parents shortly after she is born. Some women choose to take their husband's name after they are married. For example, the maiden name of Hillary Clinton (before she married former President Bill Clinton) was Hillary Rodham.
In some other cultures, such as the Hispanic culture, women do not take their husband's name. Instead, the child gets his mother's name and one of his fathers' names, as in "Gabriel Garcia Lorca", whose mother was named Garcia and whose father was named Lorca, or vice versa.