Your mother's maiden name is the same as her birth last name, which is traditionally her father's surname. Many Internet passwords and security questions ask for a mother's maiden name as it is not a commonly known feature of a woman's identity.
The term maiden in itself actually refers to a woman's marital status. If a woman is a maiden, she is unmarried and has never been married. Upon marriage, a larger percentage of women take their husband's last name. A survey done in 2011 showed that approximately 50 percent of the women in the sample supported the idea of a woman being legally required to change her maiden name.