Info Batgirl:
Bette Kane, Bat-girl
The original "Bat-girl" was Betty Kane or Bette Kane, this character was always accompanied with Kathy Kane, the Batwoman. She has little story but is rumored in the comic world to be used exclusively, with Batwoman, to refute allegations of homosexuality among the Dynamic Duo.

Barbara Gordon, Batgirl
Barbara Gordon is the daughter of Gotham Police Commissioner James Gordon. Barbara started her crime fighting career as Batgirl when she was on her way to a costume ball dressed as a female Batman. Barbara accidentally stumbles on an attempt to kidnap Bruce Wayne by Killer Moth.

Helena Bertinelli, Batgirl
When Gotham was forced to fend for itself during s Land the Huntress took up the identity of Batgirl because it inspired more fear into the heart of villians than did Huntress. When Batman found out, he allowed her to stay Batgirl until she failed to fend off Two-Face's gang. She then resumed being Huntress.

Cassandra Cain, Batgirl
Cassandra is the daughter of League of Assassin members David Cain and Lady Shiva for the purpose of creating the weapon of death. Cain raised her alone, never teaching her to speak. Instead he trained her to learn the language of the human body to become a master martial artist and assassin. This way, the parts of her brain usually used for speech were trained to see and understand people's body language and movements. As a result, she was able to almost predict what someone would do, sensing the slightest tensing of a leg before a kick or clench of a fist before a punch.

Source: wikipedia.org