HAN: Han Solo. I'm captain of the Millennium Falcon. Chewie here tells me
you're looking for passage to the Alderaan system.
BEN: Yes, indeed. If it's a fast ship.
HAN: Fast ship? You've never heard of the Millennium Falcon?
BEN: Should I have?
HAN: It's the ship that made the Kessel run in less than twelve parsecs!
Ben reacts to Solo's stupid attempt to impress them with obvious
misinformation.
Ben Kenobi may have the right idea. You see, a parsec is a unit of distance defined as the distance from the Earth to a star that has moved one arc-second (a certain distance as observed while our planet orbits the sun). It is the unit of measure for one of the oldest methods of determining astronomical distances.
Some Star Wars apologists have argued that a parsec has a different definition in this far, far away galaxy from a long time ago. Unfortunately, Dexter Jettster of the diner on Coruscant, shot down that theory when he talked to Obi-Wan in Attack of the Clones:
OBI-WAN: Well, Dex, if droids could think, we wouldn't behere, would we?
(laughing) Kamino... doesn't sound familiar. Is it part of the Republic?
DEXTER JETTSTER: No, it's beyond the Outer Rim. I'd say about twelve
parsecs outside the Rishi Maze, toward the south. It should be easy to find,
even for those droids in your archive. These Kaminoans keep to themselves.
They're cloners. Damned good ones, too.
If you want to get really scientific, one could argue that time and distance are interchangeable when dealing with astronomical scales. According to Einstein's special relativity, twelve parsecs is equivalent to about forty Earth years. Of course that assumes you are traveling close to, yet definitely slower than, the speed of light. All bets are off when you assume the fanciful hyper-luminal speeds of Star Wars space vehicles.
The best explanation to me comes from the creator himself, George Lucas. On the audio commentary track of A New Hope DVD, Lucas explains that traveling through hyperspace requires precise calculations to avoid smashing into a star, planet, black hole, or any other large object. The Millennium Falcon is able to plot some of the shortest distances possible. Thus, the ship can arrive at its destination faster than vehicles traveling longer distances.
So what the heck is the Kessel Run?
There are some variations on this story, depending on which source of the Expanded Universe you reference. The Kessel Run is a dangerous path from the planet Kessel past the Maw Black Hole Cluster. It is a space lane frequented by smugglers transporting the illegal narcotic Glitterstim spice (fictitious of course!) from Kessel.
By the way, Threepio mentioned Kessel's spice mines earlier in A New Hope while still aboard the Tantive IV blockade runner: "They're heading in this direction. What are we going to do? We'll be sent to
the spice mine of Kessel or smashed into who-knows-what!"