The Star Wars Original Trilogy cemented the franchise as a pop culture phenomenon. There were a lot of things that became iconic, but lightsabers and lightsaber duels were at the forefront. A New Hope started things off with a slow-moving duel between the villainous Darth Vader and Obi-Wan Kenobi. Since then, there have been retroactive explanations for the duel's pace. Either way, The Empire Strikes Back picked things up. Vader fought Luke Skywalker for the first time and revealed that he was the young Jedi's father.
With that game-changing revelation, Luke was forced to face his demons going into Return of the Jedi. The opening scene made fans question whether he had fallen into darkness, but it soon became clear that Luke had rejected the dark side and continued on his Jedi path. In fact, he spent the entire movie trying to redeem Darth Vader. That's why their duel in the film's last act was surprising. However, the truth is that many fans misinterpret why the duel started and who won the fight.
The fight between Vader and Luke started because the aged Emperor Palpatine goaded Luke into reclaiming his weapon. Palpatine specifically wanted Luke to strike him down in anger because that would have completed his fall to the dark side. So, when Luke retook his lightsaber, he didn't do so with the intent of fighting or killing Vader -- he only wanted to kill the Emperor.
When Luke made his move on Palpatine, Vader immediately drew his lightsaber and blocked the attack, which kept the Emperor alive, except Vader had an odd reason for doing so. The little bit of Anakin that was left inside him wanted to keep his son from falling into darkness, so he refused to let Luke kill the Emperor -- even though he would have loved nothing more than to have Palpatine dead.
When Vader instigated the duel, Luke naturally fought back. He showed that his skill had improved since their last fight, but Luke never really tried to kill his father. He disengaged a number of times and tried to convince the Dark Lord that there was still good in him. So, for a while, the duel turned into a bit of a stalemate because Luke refused to kill his father.
However, Luke wasn't the only one who refused to deal a killing blow. By this time in the story, Palpatine was pretty much done with Vader because he wanted Luke as his new and improved apprentice. So, he gave Vader some special instructions. He wasn’t supposed to kill Luke; he wasn't even supposed to beat Luke. Vader's only goal in the fight was to make Luke lose control of his emotions and bring him closer to the dark side -- and that's exactly what happened. Vader had to obey his master, so he goaded Luke until he touched the dark side. That's why Palpatine congratulated Luke, saying, "Good. Your hate has made you powerful."
Many fans declare that Luke won the confrontation because he nearly killed Vader, but that's technically not true. Vader was far more powerful than Luke and easily could have bested him. So, knowing that Vader wasn't allowed to kill Luke drastically changes the equation. His only goal was to make Luke mad, and he definitely accomplished that task. Thus, Vader didn't technically lose. He did exactly what he set out to do.