Batgirl (the modern, Barbara Gordon version) first appeared in Detective Comics #359, January 1967. (There had been a Bat-Girl character in Batman's comics before, but that character wasn't carried over into the 'new look' Batman era that began just a year and a half before.)
The character also appeared on the Batman TV show at roughly the same time, which was probably the result of creativity between DC Comics and the show's producers. Since that show was so immensely popular with kids and adults at one time, Batgirl was known to a large number of people even though her appearances in the comics were sporadic.
Batgirl was also introduced to movie audiences in 1997 with the film Batman & Robin, where she was played by Alicia Silverstone.