The Kessel Run is finally explained in Solo: A Star Wars Story. When audiences first meet Harrison Ford's Han Solo in George Lucas' original Star Wars movie, A New Hope, they are told that the Millennium Falcon is the fastest ship in the galaxy because it "made the Kessel Run in less than 12 parsecs." Those were just empty words at the time, as evidenced by Alec Guinness' unimpressed reaction as Obi-Wan Kenobi, but they're words that have lived on throughout the franchise.
While the Millennium Falcon's legend of making the Kessel Run in a record distance was touted in both the original and sequel Star Wars trilogies (so much that even Rey had heard the stories), Lucasfilm never bothered to explore the actual smuggling route on the big screen. That is, until now.
The Kessel Run & Its Problem
Right from the start, Han Solo always made it a habit of introducing the Millennium Falcon as the ship that "made the Kessel Run in less than 12 parsecs," but that statement has drawn a considerable amount of confusion over time. After all, a parsec is a measurement of length - equal to approximately 19 trillion miles (or 3.26 light years) in both real-life and Star Wars canon - not time. So, why would Han Solo use that term as proof of how fast his spaceship is? It's not like someone would claim they were the fastest runner because they ran a mile in less than 2,000 feet. It just didn't make sense.
While many fans believed George Lucas simply made an error in the script, other fans have gone to great lengths to explain the parsec's use. A common belief is that Captain Solo piloted through black holes to shorten the distance, but that was never confirmed nor alluded to in the movies. One of the wildest theories is that Han Solo and Chewbacca are actually time travelers, which is owed to the idea that, since they skirted the edge of the Maw in the Kessel Run, they were able to travel through time to make the Kessel Run via a shorter distance. Of course, these are mere theories, and Lucasfilm even had some of their own in Legends.
How Legends Explains The Kessel Run
Long before The Walt Disney Company acquired Lucasfilm, the Expanded Universe - a collection of novels, comics, video games, and various other published stories - made up the bulk of the Star Wars saga, and they were all considered canon. But, when the Mouse House came knocking, all of those stories were removed from canon and relabeled under Legends. That move angered lots of fans because those stories had, in many ways, wonderfully expanded the Star Wars universe. Plus, they provided answers to questions fans had been asking for years, not to mention explaining how Han Solo made the Kessel Run in less than 12 parsecs.
In Legends, the Kessel Run is an 18-parsec route that smugglers would use to evade the Empire when transporting spice from the planet of Kessel. The problem is, Kessel is surrounded by a cluster of black holes called the Maw. So, pilots navigating the Kessel Run would need to be cautious of their surroundings; getting too close to the Maw could tear their ship apart. Of course, Captain Solo likes to live life on the edge, so he took a shortcut through the Maw - flying close to the black holes and bending space and time, as explained in A.C. Crispin's Han Solo novel trilogy - while trying to avoid being captured by an Imperial patrol. By doing so, Han Solo was able to reduce the distance needed to make the Kessel Run by approximately 20 light years (if not more), thus setting a record.
That was the believed answer to how the Kessel Run was done in less than 12 parsecs. But, ever since Disney de-canonized the Expanded Universe, Lucasfilm has been slowly but surely reintroducing aspects of Star Wars Legends back into canon - and they are using their anthology films to do just that, including Solo: A Star Wars Story. While parts of the Kessel Run were altered from Legends for the big screen, there were some aspects that made the jump from the page, which Ron Howard and the screenwriters used to make their own mark on explaining the Kessel Run.
How Solo: A Star Wars Story Explains The Kessel Run
In Solo: A Star Wars Story, Han Solo and his team make the Kessel Run in 12 parsecs (but they're rounding down, of course, because it's more impressive), despite Lando Calrissian (Donald Glover) saying that it can't be done in less than 20 parsecs. But, in order to make up for lost time and get to Savareen before the coaxium explodes, not to mention avoid being captured by an Imperial blockade, Han Solo decides to pilot the Millennium Falcon through the maelstrom (aka the Maw), but he can't do it without L3-37. That's when Lando agrees to download L3's invaluable navigation charts into the Falcon's navicomputer (something that Screen Rant predicted early on) so that they could navigate their way through the Maw without dying... or being caught.
Solo: A Star Wars Story's explanation for Han Solo and the Millennium Falcon making the Kessel Run in less than 12 parsecs is fundamentally the same as what happened in Legends: they simply took a shortcut through the Maw. However, since going through the Maw is considered impossible, the difference in the movies is that they had the assistance of L3's navigational charts to guide them. Still, that's meant to diminish Han's skills as a pilot. Without him (and a particular move he learned from his old pal Needles on Corellia), they wouldn't have been able to avoid being shot down by the TIE Fighter pilots. Overall, though, the explanation for the Kessel Run being completed in 12 parsecs, despite it being a 20-parsec route, is because they took a shortcut through the maelstrom.