The first twenty one lines of the poem help us to understand the duke's possessiveness of his former wife: her portrait is kept behind a curtain that none are allowed to draw aside except him.  We can also learn that his pride was, perhaps, wounded by the fact that it was not only "Her husband's presence" that prompted her to blush; she, apparently, was pleased by anything else as much as she was by his attention to her.  

The duke also seems to place a lot of importance on appearances, as he name drops "Fra Pandolph," a famous painter who is renowned for producing excellent likenesses of individuals.  The duke seems to want his auditor to know that he paid dearly for this painting and demanded only the best.  In fact, he mentions the painter's name even before he begins to describe the woman who used to be his wife.  He prioritizes the value of the painting over the value of its subject.