Han Solo is the ultimate cowboy and no BS character in Star Wars. He also happens to be the pilot of the fastest hunk of junk in the galaxy - the ship that made the Kessel Run in less than 12 parsecs. Now, he may not use the term correctly (a parsec is a unit of distance), but in our minds it represents a no frills space ship that can travel faster than anything else in the galaxy. At Parsec, we're all about shaving milliseconds off of our video stream, and we want to keep it dead simple. So for that reason, we named our company Parsec.
And the other interpretation is that Han Solo actually navigated through the Kessel Run in 12 parsecs, i.e. he found the shortest path. Either way, Parsec means fast as hell and we make big distances shorter. Also, we like Star Wars, Star Trek, and all things stars.