In Episode IV: A New Hope, Han Solo convinces Obi-Wan that his ship is fast enough to get to Alderaan by saying: "You've never heard of the Millennium Falcon?... It's the ship that made the Kessel Run in less than twelve parsecs."
But the parsec is a unit of distance, not time, equivalent to about 19 trillion miles or 3.26 light-years. How could a hot-shot pilot like Han make such a rookie mistake? Here are a few possible explanations.
1. Lucas Made an Error
The most obvious explanation is that George Lucas didn't do the research. Many sci-fi universes have their own invented time units, such as microts (seconds) in Farscape and yahrens (years) in the original Battlestar Galactica.
"Parsec" sounds vaguely like "second," so maybe Lucas intended it to be an exotic-sounding time unit that didn't imply any particular length of Earth time. He simply missed the fact that the parsec is a real unit of measurement.
One could argue that the parsec is a unit of time in the Star Wars universe. The Expanded Universe, however, establishes time units with the same names as their real-life counterparts.
2. Han Solo Lied
Another possibility is that Han was just making stuff up. He had a price on his head and needed money fast -- and here were these two apparent yokels needing a ride. Although Luke Skywalker claimed to be a good pilot, Han probably thought he was bluffing to bring the price down.
By making a seemingly nonsensical claim -- essentially that the Millennium Falcon "ran the 100-yard dash in 100 yards," as Jeanne Cavelos writes in The Science of Star Wars -- Han could have been testing his potential customers. If they bought the story, he could assume they were ignorant about space travel and try to charge them more.
The incredulous look Luke gives in response to Han's claim might support this theory. It's also how George Lucas explains the line. Like the previous explanation, however, this is not supported by the Expanded Universe.
3. Han Took a Shortcut
The Expanded Universe puts forth the most interesting and thorough explanation to the "parsec problem": the Kessel Run was normally an 18-parsec route. A popular travel route for smuggling operations, the Kessel Run went around the Maw, a cluster of black holes.
Han's claim to have made the Kessel Run in less than 12 parsecs was therefore not just a boast about his ship's speed, but also his skills and daring as a pilot. Han shaved a third of the distance -- and precious time -- off the normal route by flying dangerous close to the black holes.
This explanation is detailed in A.C. Crispin's Han Solo Trilogy. In "At the Crossroads: The Spacer's Tale," the bounty hunter BoShek beats Han's record, although this feat isn't as impressive because he didn't have a cargo in tow. Don't worry -- our fearless bounty hunter retook the record in the comic strip The Second Kessel Run.