Let me break it down for you because this is something everyone should know.
See, Kessel is a planet known for producing spice. Not spice that you put on food, but spice that you consume like a drug. There are different kinds and Glitterstim Spice is one of the most valuable. It can give you temporary euphoria and telepathic powers. It’s tightly regulated by the Empire (and later the New Republic).
The Kessel Run is a smuggling run. It takes the smuggler very close to The Maw Cluster. The Maw is an unstable region of space made up of a bunch of black holes. It’s extremely dangerous to get close to black holes because they can suck you in. The Maw Cluster sits as an obstacle between where the smuggler is, and the planet Kessel.
Are you following so far? Good. See, the Imperials patrol all the normal hyperspace lanes and use Interdictor Cruisers (which generate gravity wells that simulate those of a planet) to pull ships from hyperspace when needed. They can then keep these ships trapped in normal space, preventing them from fleeing, while they board them and do what amounts to customs checks.
This is why smugglers attempt the Kessel Run in the first place. To avoid Imperials. It is typically a journey of more than 12 parsecs, depending on how close you are willing to get to the Maw and it’s black holes.
What Han Solo is trying to get across when he says that the ship made the Kessel Run in under 12 parsecs is that his ship is so damn fast and that he is such a fantastic pilot that it was able to skim closer to the Maw than anyone else, shaving both time AND distance off the trip. He was able to accomplish this because he was less worried about not being able to achieve escape velocity from the black holes he was getting closer to, because of how fast the Falcon is. Thus, due to the speed of his ship, he was able to make the Kessel Run in a distance of under 12 parsecs.