Kui was one of Frieza's henchmen, as well as Vegeta's old rival. He was in charge of operations on Frieza Planet #79. He is the one who led the attack on Planet Rito, and murdered Bun's parents right before the youth's eyes.
After his battle with Goku, Vegeta came to Planet #79 for medical treatment. It is here he ran into Kui, who warned him to stop pursuing his own selfish ambitions, or face the wrath of Frieza. When Vegeta went renegade, Kui followed him to Namek, with orders from Frieza to kill him. However, since he had grown stronger since his fight with Goku, Vegeta easily killed Kui.