What is the meaning of mother's maiden name?

Answer 1

Your mother's "maiden" name is the last name that she was born with, or her last name before she was married

Answer 2

Traditionally in the English-speaking world, a child uses the family name of the father. Also traditionally, when a woman marries, she takes the family name of her husband. At that point the family name she used to use, the family name of her father, is called her "maiden name" because it was her name when she was a maiden.

Your mother's maiden name is usually the surname (or family name) of your maternal grandfather.