The first ever lightsaber duel in the Star Wars franchise was the showdown between Darth Vader and Obi-Wan Kenobi aboard the Death Star in Star Wars: Episode IV - A New Hope. After shutting down the Death Star's tractor beam so that the Millennium Falcon could escape, Obi-Wan encountered his former Padawan for the first time in years. They immediately ignited their lightsabers, and Vader proclaimed, "I've been waiting for you, Obi-Wan. We meet again at last. The circle is now complete. When I left you, I was but the learner. Now, I am the master." Obi-Wan retorted, "Only a master of evil, Darth." After this brief exchange of words, they began their battle to the death. Despite the Sith Lord's gloating, he and his old teacher seemed evenly matched throughout the fight.
Yet, once Obi-Wan saw Luke Skywalker and his companions making their way to the Millennium Falcon, he gave up on the duel. With a knowing smile, he assumed a defenseless position and allowed Vader to cut him down. As he died, his body vanished into thin air, leaving only his cloak and lightsaber behind. This dramatic scene brought the film's heroes to their lowest point before the final act, but why did Obi-Wan decide to sacrifice himself? With some luck, he might have bested Vader as he had in their earlier duels, or at least fended the Sith Lord off for long enough to find a means of escape. The film did not answer this question directly. Still, there were several reasons for Obi-Wan to let Vader win in A New Hope, and his choice was instrumental to the Rebellion's ultimate victory over the Galactic Empire.
Obi-Wan's Death Strengthened His Connection to the Force
The first reason was one that Obi-Wan alluded to earlier in the fight when he said, "If you strike me down, I shall become more powerful than you can possibly imagine." This memorable quote referred to becoming a Force ghost, or Force spirit, an advanced Jedi technique that Qui-Gon Jinn had taught Obi-Wan from beyond the grave. Rather than entirely becoming one with the Force, as usually happened to a Jedi after death, Obi-Wan was able to maintain his identity and manifest in the universe to continue guiding Luke. Ironically, by killing Obi-Wan, Vader essentially made him immortal. As a Force ghost, he was no longer confined either to his aging physical body or the restrictions of space and time; he could appear wherever and whenever he needed to, be it the harsh tundra of Hoth or the remote swampland of Dagobah.
Obi-Wan did not appear as a Force ghost until Star Wars: Episode V - The Empire Strikes Back, but A New Hope laid the groundwork for it. Almost immediately after Obi-Wan's death, Luke heard his voice in his head, urging him to run from Vader and the stormtroopers. Later, in the film's most iconic scene, he advised Luke to "use the Force" instead of his targeting equipment during his trench run on the Death Star. In The Empire Strikes Back, he finally appeared as an apparition before Luke and told him to seek out Yoda. He later convinced Yoda to give Luke a chance even though he was much older than usual Padawans. Obi-Wan could have shared some of this advice and information while he was alive, but it would have been more difficult. Unless he accompanied Luke in person -- which would have been impossible in a single X-wing -- he would have needed to use a comlink or holoprojector, both of which were prone to malfunction or interception by the Empire. This leads to another, more practical reason for Obi-Wan's sacrifice.
Obi-Wan's Sacrifice Saved Luke's Life
Defeating Vader was not Obi-Wan's goal during their duel. While he surely would have taken the opportunity if it presented itself, his top priority was distracting Vader. He needed to buy time for Luke and the others to rescue Leia and get to safety, preferably without Vader realizing that his son was there. One of Luke's most consistent character traits throughout the Star Wars series was his willingness to throw himself into danger to protect the people he cared about. Therefore, Obi-Wan knew that if he prolonged the fight, Luke would step in and try to help him.
This would have ended in disaster, as Luke was no match for a Sith Lord at that point. Even after training with Yoda in the next film, he lost his duel with Vader in Cloud City. Obi-Wan wanted to end the fight as quickly as possible so that Luke would have no reason to engage Vader, and the easiest way to do so was to let himself die. That was not the only benefit of ending the confrontation early; if Obi-Wan had battled to the point of exhaustion, Vader might have captured him instead of immediately killing him. The Empire then could have interrogated him and gained valuable information about the Rebellion.
Obi-Wan Set a Strong Example for Luke
Obi-Wan's sacrifice also had psychological effects on both Vader and Luke. He believed that he had no chance of beating Vader, but he could at least lose on his own terms. For nearly two decades, Vader had been dreaming of vengeance against Obi-Wan. He wanted to inflict the same pain that he had felt after his loss on Mustafar upon his old master. But by refusing to put up a fight in the end, Obi-Wan denied him this catharsis. Vader did not get the satisfaction of outperforming him in a fair duel, nor did he get to draw out his suffering; Obi-Wan died from a single, clean stroke. Perhaps he also held out hope that the emotional turmoil of killing his former friend would get through to what remained of Anakin Skywalker deep within Vader. But even more importantly, Obi-Wan's death inspired Luke. Watching his mentor die at Vader's hands gave him even more of a personal stake in seeing the Empire vanquished. It also demonstrated the power of the Force to Luke and showed him that death is not something to fear when the time comes.
Obi-Wan had never been confident in his skills as a teacher. He was barely a Jedi Knight himself when he took Anakin on as his Padawan, and he struggled to live up to the example of Qui-Gon. Both Star Wars: Episode III - The Revenge of the Sith and the Obi-Wan Kenobiseries made it clear that he blamed himself for Anakin's eventual fall to the Dark Side. By making the ultimate sacrifice for his new student, he found redemption for this perceived failure. He had already trained Luke in the basics of the Jedi way, and he knew that the greatest of all Jedi Masters was available to teach him the rest, so Obi-Wan felt that he would be more valuable to Luke in death than in life. In the end, Obi-Wan's guidance was successful. Luke was victorious in Star Wars: Episode VI - Return of the Jedi because he chose not to give in to violence when dueling his father. Obi-Wan's Force ghost could feel proud of Luke, both for overthrowing the Empire and for bringing Anakin back to the light.