The Infinity was a fast smuggling ship that the Human smuggler BoShek piloted to Tatooine in 0 BBY in order to deliver it to the Mos Eisley "monastery" to change its transponder codes. According to the smuggler, it was this ship which he used to break Han Solo's Kessel Run record. But that record was beaten again by Han Solo with the Millennium Falcon a few months later.
Behind the scenes
Infinity was also the name of a server - or "Galaxy" - in Star Wars Galaxies.