There have been several versions of Supergirl, but the best-known incarnation is Kara Zor-El, Superman’s cousin.
Crisis on Infinite Earths features Supergirl's heroic death. After Crisis, Superman was the sole survivor of Krypton's destruction. For nearly 20 years, the title of Supergirl was given to several different characters who are not Superman's cousin; however, a post-Crisis version of Kara Zor-El was re-introduced into modern continuity.
Current Supergirl:
Kara Zor-El
Varations of Supergirl:
Power Girl
Matrix
Linda Danvers
Cir-El