Jack was employed into service for the East India Trading Company and was given command of the Wicked Wench. However, after he set free a cargo of slaves, his employer, Cutler Beckett, had Jack branded as a pirate and the Wench set aflame and sunk. After failing to rescue the Wench, Sparrow struck a bargain with the ghostly captain of the Flying Dutchman, Davy Jones, to resurrect his beloved vessel. Jones returned the ship to Jack in near perfect condition except for the permanently charred hull. This prompted Jack to rename her the Black Pearl.
Jack Sparrow just got way cooler.
Yo, this is why Norrington said he’s the “worst pirate I’ve ever heard of,” and then Jack followed it up with, “But you have heard of me.”
Because Jack was branded a Pirate because he freed people rather than stealing anything. So Norrington, with his sense of duty, knows that Jack has been branded a criminal for actively not being a terrible human being. Norrington is torn between his duty as a naval officer and knowing that Jack is right.