The Duke of Ferrara is negotiating with a servant for the hand of a count’s daughter in marriage. (We don’t know anything about the Count except that he is a count. And that he’s not the Count from Sesame Street – different guy.) During the negotiations, the Duke takes the servant upstairs into his private art gallery and shows him several of the objects in his collection.
The first of these objects is a portrait of his "last" or former duchess, painted directly on one of the walls of the gallery by a friar named Pandolf. The Duke keeps this portrait behind a curtain that only he is allowed to draw. While the servant sits on a bench looking at the portrait, the Duke describes the circumstances in which it was painted and the fate of his unfortunate former wife.
Apparently the Duchess was easily pleased: she smiled at everything, and seemed just as happy when someone brought her a branch of cherries as she did when the Duke decided to marry her. She also blushed easily. The Duchess’s genial nature was enough to throw the Duke into a jealous, psychopathic rage, and he "gave commands" (45) that meant "all smiles stopped together" (46). We’re guessing this means he had her killed although it’s possible that he had her shut up somewhere, such as in a convent. But it’s way more exciting if you interpret it as murder, and most critics do.
After telling this story to the servant of the family that might provide his next victim – er, sorry, bride – the Duke takes him back downstairs to continue their business. On the way out, the Duke points out one more of his favorite art objects: a bronze statue of Neptune taming a seahorse.