Grand Moff Wilhuff Tarkin is the elderly Imperial in charge of the Empire's first Death Star. About as evil and bloodthirsty as they come, Tarkin is the man responsible for the destruction of Princess Leia's homeworld of Alderaan with the Death Star's super-duper laser of ultimate doom, and carries such political influence and favor with Emperor Palpatine himself, that he could even boss around Darth Vader.
Tarkin's next course of action is to destroy the Rebel base on Yavin IV, again employing the Death Star's awesome destructive power. The Rebels will not go down without a fight however, and attack the Death Star with their X-Wing fighters in an attempt to hit the superweapon's sole weak spot.
During the battle, another Imperial officer named Chief Bast informs Tarkin of the Rebel's intended target and asks the Grand Moff whether they should evacuate. Nonplussed, Tarkin responds with his famous final words: "Evacuate? In our moment of triumph? I think you overestimate their chances."
Cut to: Outside the Death Star. Luke, using the Force, targets the Death Star's weak spot as Darth Vader closes in in his TIE Fighter. He has him in his sights but is stopped from killing the young Padawan by a triumphantly returning Han Solo. With the Sith Lord taken care of, Luke follows Han's advice to "blow this thing and go home," and he fires. Using the force for insight, the exhaust pipe [the Death Star’s weak spot] is hit. At this moment, the Death Star targets Yavin IV as Tarkin anxiously watches from the control room, stroking his chin as the voice on the P.A. system announces, "Stand by. Stand by" as the super-duper laser prepares to fire. The Death Star is then destroyed by a single, massive internal explosion that blows it apart from the inside out mere seconds before it can fire, instantly killing everyone aboard, including the too-proud Grand Moff Tarkin.