I’ve heard the discussion about Han Solo’s famous “Kessel Run” time and time again - both inside the Star Wars community and outside it. Common consensus seems to be that Han Solo’s boast that the Falcon could do the run in 12 parsecs indicates that Solo has no idea what a parsec is, or else relies on the fact that his audience doesn’t know.

This discussion relies on two main facts:

1. A parsec is a unit of measurement equivalent to roughly 3.26 light-years. This means that a parsec is a unit of distance, not a unit of time.
   
2. The Kessel Run is a smuggling route in the Star Wars universe, running illicit spice from the spice mines of Kessel to its destination worlds. It is not a commonly-used trade route, partially because the route is fraught with danger - especially “The Maw” cluster of black holes.

The main mistake people seem to make when discussing this issue is believing that Han is boasting about the Falcon’s speed. This is understandable, because Han often boasts about the Falcon’s speed in other situations, and it is natural to assume that a vehicle owner boasts about the speed of their vehicle because that is what we Earthlings are used to when discussing cars and other machines.
As such, they think that Han is purporting that “12 Parsecs” is a quantification of the Falcon’s immense velocity.

This is an incorrect assumption, however. What Han is actually boasting about is the Falcon’s ability to safely navigate the dangerous Kessel Run by the shortest possible route.
Travelling at hyperspace is not a simple matter of moving the ship directly from A to B, since there are doubtless hundreds or thousands of intervening planets, stars, asteroids, and other dangers. A ship’s computer must be programmed with a route which avoids such obstacles - usually giving them a wide berth, just to be on the safe side. The computer can also adjust itself en route if an unforeseen hazard presents itself.

Han Solo programs the Falcon’s computer system to fly as close to these hazards - especially the forbidding Maw Cluster - as is possible without being destroyed. Most other pilots would see this behaviour as foolhardy, but Han apparently doesn’t care. Because the Falcon is programmed to fly closer to these obstacles than most other pilots would dare consider, it needs to “steer” far less, and so can traverse the route in a straighter line than any other starship. This means that the Falcon completes the Kessel Run in a shorter distance than other ships - a mere 12 parsecs.

This is backed up in The Force Awakens when Rey, impressed that the ‘hunk of junk’ she’s aboard is the Millennium Falcon, marvels that “This is the ship which ran the Kessel Run in 14 parsecs”. Han corrects her by saying “12″. This therefore implies that 12 parsecs is more impressive than 14 - something which is totally in keeping with the above.

Han isn’t talking out of his arse when he boasts about the Falcon’s record, nor is he demonstrating his lack of understanding of interstellar measurements. He’s just not talking about what many people think he’s talking about, which is their own lack of understanding, not Han’s.

Aries: Han Solo
Taurus: Rey
Gemini: Princess Leia
Cancer: Finn
Leo: Poe Dameron 
Virgo: Padmé Amidala
Libra: BB-8
Scorpio: Kylo Ren
Sagittarius: Anakin Skywalker
Capricorn: Obi-Wan Kenobi
Aquarius: Yoda
Pisces: Luke Skywalker