Chronology of Star Wars

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That sir, is a nice find.

It's not nice, it's awesome!

I've only just found out that Parsec is a unit of distance and not time

One parsec equals 3.26 light-years, or 19.2 trillion mi (30.9 trillion km)

Yep which makes Han's comment make just as much sense, he's saying he completed the Smuggling Run (The Kessel Run) in the shortest amount of distance whereas most people assume he means he did it in record time

It's something to do with The Maw he's saying he navigated through the Maw.

Yes, there is no clear and definite hyperspace road around the Maw because of the gravitationnal mass of the black holes that troubles hyperspace (remember one cannot jump in hyperspace near a planet because of its mass). As there is no clear road, smugglers have to calculate and do jumps themselves. Han Solo managed to calculate jumps to travel through less parsec than the usually used road.
Of course, a shorter road equals a faster travel.

I do believe this has been explained in one of the books of The Han Solo Trilogy