The King and Duke are con men who earn money by swindling people out of money. In each town they visit, they concoct a scheme to sham people out of money. We see the pair do this in a variety of ways. They print up play bills claiming to be great actors and then put on disappointing shows only to quickly skip town. One goes to a revival claiming to be a pirate, claims to see the errors of his ways, and then publicly announces he is going to save other pirates as his new life mission. The town members subsequently raise an offering for the con man.
The two men always claim to be something they or not, as we see in their false claims to be royalty and as we see in their false claims to be the brothers of a recently deceased wealthy man, and their mission is to essentially rip people off.