After he struck Obi-Wan Kenobi with his lightsaber during their duel in the original Star Wars film, Darth Vader was confused when his former master's body disappeared in thin air — why? Released in 1977, the first installment from George Lucas' famed space opera introduced the narrative's main heroes: Luke Skywalker, Leia Organa, and Han Solo. But the movie also debuted its mentor figure in the Jedi Master Obi-Wan whose story more properly played out in the prequel films.
While Star Wars didn't reveal much about Obi-Wan considering his limited screen time, he was extremely important to the narrative. Had it not been for him, Luke wouldn't have joined the Rebellion's fight against the evil Empire; the same could be said with regard to Han and Chewie. But ultimately, his biggest impact in the story when he sacrificed himself to ensure the safe escape of the young heroes from the Death Star. Seeing that the Skywalker twins Luke and Leia were finally reunited, he knew that there was a higher chance that the Rebellion would win with Luke and Leia working together; it's also worth noting that he's one of the very few people who knew that they were related.
So, although Darth Vader and Obi-Wan's lightsaber fight in A New Hope was less thrilling than other duels, there's so much narrative weight on it. For starters, it further motivated Luke to help the Rebellion. It also marked the first time that the former friends/allies were reunited after years of being separated. However, despite his time learning the Jedi code when he was still Anakin Skywalker, Darth Vader appeared to be befuddled when his former master disappeared on thin air upon being struck by his lightsaber. At this point, Obi-Wan intended to sacrifice himself, so he was ready to be killed knowing that he could be more powerful when he died as he had learned how to linger via being a Force spirit. Darth Vader didn't know about this particular skill because it was a practice that was long forgotten and was rediscovered by Qui-Gon Jinn. Given this, the Sith Lord couldn't believe that Obi-Wan vanished when he died — perhaps, even dubious at first about whether or not he's really gone.
Since Qui-Gon was the first contemporary Jedi to start tapping into this particular skill, his spirit communicated with Jedi Grandmaster Yoda and Obi-Wan, guiding them as to how one can retain their consciousness after becoming one with the Force and even manifesting themselves physically. It's the reason why in their respective deaths, their bodies faded, although Darth Vader only witnessed Obi-Wan's disappearance. Eventually, after the Sith Lord's redemption in Return of the Jedi, Anakin ultimately learned the secrets of becoming a Force Ghost, something that his predecessors may have very well taught him.
The iconic duel between former friends is expected to get additional context thanks to the upcoming Obi-Wan Kenobi series on Disney+. Lucasfilm confirmed that Hayden Christensen will be back as the Sith Lord, setting the stage for another encounter between him and the titular character. This means that Darth Vader and Obi-Wan's Star Wars reunion on the Death Star wasn't their first following their falling out on Mustafar, though it's unlikely the Jedi will reveal any secrets about death to the Sith Lord.