Kara Zor-El is the daughter of Superman's uncle Zor-El and his wife, Alura. Biologically, Kara is older than Kal-El (Superman); she was a teenager when he was a baby. However, after an attack on Krypton by Brainiac, she was sent off in a rocket towards Earth. Unfortunately, her rocket was caught in a meteor. She arrived to Earth years after her cousin did.
In other incarnations, Kara was retconned to being the last survivor of Argos, the sister planet to Krypton, so that Superman could stand as the sole survivor of Krypton. With this, her name would be Kara In-Ze. (In-Ze being the last name of her mother, Alura.)
In some television media, such as in the DC Animated Universe by Bruce Timm, Supergirl was portrayed by the Kara In-Ze likeness, with some slightly changed backgrounds