A sidekick of Vegeta in the manga/anime Dragonball Z. He's a pretty tough customer, and really puts the hurt on Piccolo, Krillin, Gohan, Yamcha, Tien, and Choutzu after he and Vegeta land on Earth in search of the Dragonballs (actually, he kills all of them except Krillin and Gohan).
A few hours after they arrive, Son Goku arrives to fight (up until this point he had been dead - the Dragonballs were used to bring him back). Goku plays with Nappa for a good 5 minutes before Vegeta orders him to stop.
Nappa is furious that he has to stop; despite the fact that, in actuality, he was totally outclassed by Goku, he was arrogant enough to think he could win. He decides to kill Gohan and Krillin to make himself feel better. To save them, Goku had to use the Kao Ken (Lit: "Fist of the World") technique, which increases his power and speed several times over, but only for a very short time. He quickly catches up with Nappa and breaks his back. A moment later, Vegeta kills Nappa, because he is of no more use as a fighter. Vegeta is a bad man.
We don't find out much more about him in Toriyama's writings, but the Bardok TV Special shows that he had been Vegeta's companion/bodyguard since Vegeta was quite young.
Nappa means "cabbage", part of the joke involving Saiyan (or Saiyajin) names.