Han boasting that the Millennium Falcon is the ship that made the Kessel Run in 12 parsecs has been the cause of much confusion and debate among fans for the last 40 years. The question arises because a parsec is a measure of distance not time, so Han boasting about the speed of his ship by saying that it was able to complete a route over the shortest distance makes little sense.
In Legends, the explanation for why records for the Kessel run were measured in distance rather than time was that the planet Kessel was very near to a cluster of black holes known as the Maw. The fastest route meant cutting it very close to the black holes. The faster the ship, the closer it could safely fly to the Maw. The Falcon is the fastest hunk of junk in the galaxy, so it was able to fly closer to the Maw than any other ship and thus attained the record for the shortest Kessel Run.
The teaser for the new Solo stand alone film seems to hint at the Maw being reintroduced to canon in some fashion. In this scene we see a Star Destroyer flying through what appears to be a storm in space.
We also see the Falcon flying through what appears to be the same storm.
The potential re-canonization of the Maw as the reason for the Falcon attaining its 12 parsec record has some interesting implications for the Sequel Trilogy as well. The Unknown Regions were shown in the Aftermath novels to be a region of space that is full of all sorts of weird space time anomalies. The Falcon just so happens to be on Jakku at the opening of The Force Awakens, having been stolen from Han years before. The planet Jakku is the jumping off point for entering the Unknown Regions, which is why Palpatine had the observatory built there according to the Aftermath novels. What if whatever it is that allows the Falcon to make the Kessel Run in 12 parsecs also makes it uniquely capable of navigating the Unknown Regions? What if that’s why Ducain, the Irving Boys, and Unkar Plutt made the modifications to the Falcon that they did? Perhaps they were trying to make it better able to navigate through the Unknown Regions for some reason.