Luke Reunited with Biggs
In this scene, Luke reunites with his friend Biggs at the rebel base hanger before they attack the Death Star. They are then greeted by Blue Leader (who in the final film became Red Leader, and his canon name is Garven Dreis). Dreis asks Luke if he has been cleared to fly an X-Wing, to which Biggs responds, “Luke is the best bushpilot in the outer rim territories.” Dreis then says he once flew with Luke’s father, and that if Luke is half the pilot his father was, he’ll do all right. Biggs and Luke then say they have a lot of stories to share, and they’ll share them when they get back from the Death Star assault.
Tragically, Biggs subsequently dies in the battle before he and Luke have a chance to share their stories.
Why it was cut
There is no direct evidence of why this scene was cut. Given that the earlier scenes with Biggs were cut though, it makes sense that Lucas and editors would decide to cut the scene that was meant to give payoff to those earlier scenes. This meant that Biggs’ only inclusion in the 1977 film is in the Death Star assault, which gives his death less impact than it would otherwise. Aside from that though, the only other information conveyed in this scene is more context for why Luke is now able to fly for the rebellion and a reminder that Luke’s father was a great pilot, which Obi-Wan already told Luke earlier in the film.
Lucas later reinserted this scene into the 1997 special edition, despite still not including the earlier scenes with Biggs on Tatooine. However, in this version he cut Dreis’ dialogue about flying with Luke’s father, as by that point Anakin Skywalker’s backstory was much more developed, including the fact that Anakin became Darth Vader, and Lucas was already developing the Star Wars prequel trilogy. Perhaps Lucas decided Anakin flying alongside Dreis did not make sense given the story he was writing for the prequels.
 Garven Dreis ended up flying alongside Anakin Skywalker during the Clone Wars in a story published in a 2003 issue of Star Wars Insider, the official Star Wars magazine. While this story is now considered part of the Star Wars Legends continuity and not the ‘official canon’ that Lucasfilm now publishes, this story does corroborate Dreis’s claim that he flew alongside Luke’s father. Wookieepedia contributors, “Garven Dreis (Legends),” Wookieepedia, The Star Wars Wiki, https://starwars.fandom.com/wiki/Garven_Dreis/Legends?oldid=11151315 (accessed December 11, 2021).