This is just a theory, but I feel like it makes sense, hope you all agree.
"You've never heard of the Millennium Falcon?…It's the ship that made the Kessel Run in less than twelve parsecs."
The Kessel Run was a hyperspace route used by smugglers and unscrupulous freighter captains to move spice from the spice mines of Kessel at the behest of the Pyke Syndicate, who relied on the foolhardy Kessel Runs to deliver the illicit substance to their customers. Han Solo, captain of the Millennium Falcon, made the infamous run in less than twelve parsecs, breaking a long-held record.
As some people have pointed out, a parsec is in fact a unit of distance, not time, claiming that Han's boast doesn't make sense. I say it makes perfect sense, the nerds are simply focusing on the wrong word, specifically suggesting the claim refers to the Falcon's speed.
Don't get me wrong, the Millennium Falcon is easily one of the fastest ships in the galaxy, at least for it's size, but speed wasn't the only factor here.
With this, we have to consider the fact that whatever the ship, when traveling at lightspeed, they all travel at the same speed. This is ignoring Han's claim that "she can make .5 past lightspeed", not to mention any ships capable of ludicrous speed, of course.
Q. What is the shortest distance between two points?
A. A straight line.
You have to remember that lightspeed travel requires destination planning, "it ain't like dusting crops", but a better (albeit boring) analogy would be that it's like a game of golf, especially in regards to the Kessel Run.
The criminal endeavor of smuggling spice suggests a good deal of avoiding Imperial or otherwise police involvement, so the more treacherous and less traveled the route, the better. This is where the Falcon's actual speed comes into play. I haven't found anything yet that confirms this theory, but it makes sense that the Kessel Run is fraught with such hazards as asteroid fields, and Imperial patrols, and as such, any pilot wanting to avoid those things would do best to take whatever long way around they can find. When playing golf, the obvious goal is to get the ball to the hole in as few swings as possible, but if you want to avoid sand traps, you aim your shots around them.
The idea here, is that Han went right through them.
The Millennium Falcon's default speed & maneuverability, paired with his expert piloting, contributed to his success in traversing the hazards & completing the Kessel Run in a shorter traveled distance (and presumably, time) than anyone before him; less than twelve parsecs.