A bat mitzvah is a "daughter of the commandments". (Alternative spelling and pronounciation is bas mitzvah.) It signifies someone old enough to be morally responsible for her own actions.
The "becoming of age" is often celebrated by the young woman leading a religious services at age 12 or 13. However, even without the ceremony, she is a bat mitzvah and religiously responsible for her own actions.
The more traditional branches or denominations of Judaism usually use 12 as the age for a girl, while other branches, such as Reform, use 13, the same age as for a boy. In more traditional cultures, the girl will not lead a religious service or read from the Torah.
In modern day U.S. Jewish cultures, the bat mitzvah is often celebrated with additional receptions and parties.
The related term for a boy is Bar Mitzvah.