In the original Star Wars trilogy, Luke Skywalker and R2-D2 have several interactions together, but it's not entirely clear how the Jedi learned to understand what the astromech droid is saying. Droids have always been a key component of the Star Wars franchise, with some of them being so intelligent they can speak multiple languages, such as R2's companion, protocol droid C-3PO. Artoo, however, has only ever spoken in the default droid language known as "Binary," which contains a mixture of whistles, chirps, and beeps, both loud and quiet. For this reason, Luke initially relied on C-3PO to translate whatever the droid said to him.
Early in The Empire Strikes Back, however, while Luke pilots his X-Wing through space, the two communicate more easily. Luke appears to use a central panel inside his cockpit, which provides him with an on-screen translation of whatever Star Wars' R2-D2 says. That said, Luke spent much of his childhood with droids, living with and fixing them up. He seemed to pick up on their language rather more quickly than a normal human could. It's likely that Luke learned the droid language over time and simply interpreted the sound of Artoo's beeps and different mannerisms to get a sense of his emotions and what the droid was trying to communicate.
When Did Luke Start Understanding R2-D2 (Without A Translator)
During preparation for the attack on the first Death Star, Luke boards his X-Wing and asks a nearby R2-D2 if he's okay. The droid responds with a high-pitched, positive-sounding beep, and Luke clearly understands that the little droid is replying in the affirmative. It makes sense why, prior to this moment in A New Hope, Luke couldn't grasp anything R2 said. He was still fairly new to the droid's mannerisms, slowly picking up on small phrases and sentences.
After the original Star Wars, Luke understands R2-D2 better than ever, so much so that the Jedi Master has full-on conversations with the droid. By this point, there's no question that he's fluent in the language. Although not explained on-screen, given Luke's history with droids and the fact that the original trilogy takes place across a four-year period, it's probable that Luke simply learned Binary over time. This would explain why he's suddenly able to understand Artoo without C-3PO's help in The Empire Strikes Back and Return of the Jedi.
Other Characters That Can Understand Droids In Star Wars
All droids speak and understand Binary, given it's their first language. But only a few of the human characters in Star Wars can understand droids; Luke Skywalker wasn't the only one. Obi-Wan Kenobi was another human who could speak Binary, as well as Anakin, who shared the strongest relationship with R2-D2, as seen in the prequel trilogy and Star Wars: The Clone Wars. Even canon characters such as Hera Syndulla, Ahsoka Tano, Princess Leia, Rey, and Poe Dameron can understand the language droids speak as they've all had to interact with them in one way or another. Binary might seem like a complex language, but by incorporating it into Star Wars, the story truly has a sci-fi feel for audiences to explore.