Star wars: The portrayal of minority and female characters

[Cyberman]

And Parsec is a unit of distance not time.

To Lucas' credit, he explained this one in commentary. In the Star Wars universe, ships can't travel through hyperspace in straight lines because they have to avoid collisions with objects (planets, moons, stars, etc). The Millennium Falcon's navigation computer was superior to other ships of its class, and could plot shorter routes between the same two points via hyperspace. So the boast that the ship can make the Kessel Run in less than twelve parsecs is basically a boast that the ship can get through hyperspace faster than most ships because it can calculate shorter routes. The Kessel Run isn't a set route via hyperspace, and presumably most ships have to fly more than 12 parsecs in order to complete the run.

There's an alternative explanation in the expanded universe which states that the Kessel Run is a popular route for smuggling operations, and is usually 18 parsecs long, because you have to navigate around a cluster of black holes and pilots don't want to fly too close to them. Solo's boast is a way of telling people that he is such a daring (and skilled) pilot that he managed to shave over 6 parsecs off the route by flying dangerously close to black holes.

There's a simpler explanation in the shooting script. After Han boasts about the parsecs thing, there's a stage direction to the effect of "Ben reacts at the obvious disinformation". You can see Alec Guinness doing this in the scene; he gives a sort of "I can't believe you just said that" look.