Points is a member of Falstaff's gang.
Real World Background
Points is named after Poins, one of Falstaff and Prince Hal's friends in Shakespeare's Henry IV plays. (Greg Weisman altered the name slightly from its Shakespearean original to stress Points' sword-fighting skills.) In Henry IV Part One, Poins informs Falstaff and Prince Hal about the wealthy travelers passing Gadshill in Kent whom they can rob; afterwards, he privately suggests to Hal that the two of them rob Falstaff and the rest of the gang after they had robbed the travelers, for a lark. Hal agrees to this, and together they surprise and rob Falstaff and his men; afterwards, they listen to Falstaff's comically exaggerated account of the battle.
In Henry IV Part Two, Poins and Prince Hal spy on Falstaff and Doll Tearsheet as they dine together, in an echo of the Gadshill prank. After this scene, Poins fades from the play, never receiving a formal rejection from Hal unlike Falstaff and the rest of his company.