Lurtz is the name given to the first Uruk-Hai in the movie The Fellowship of the Ring. His first act was to kill the first thing he saw, one of Saruman's orcs. He was a creation that came about from the breeding of orcs with goblin men.
Lurtz was the appearant leader of the Uruk band sent forth to capture the halflings and slay the rest of the Fellowship. He stood next to Saruman when he was rallying the Uruk-Hai and was the one yelling "Find the halfings!" when they tracked down the Fellowship.
Lurtz was the one who used ballista sized arrows to slay Boromir. He then fought and lost his head to Aragorn.
Lurtz was never mentioned by name in JRR Tolkein's The Fellowship of the Ring nor was his name uttered in the film. His name can be found on a host of merchandise including action figures, collectible card games and porcelain busts