Here the Duke (the 'I' of the poem) is showing the picture of the Duchess to his guest and explaining that he alone is allowed to pull back the curtain that covers it from view. He talks about how beautiful it is; 'a wonder' and how it was painted by Fra Pandolf and is so skillfully done that she almost looks alive. This is irony considering that later on in the poem we find that the Duke has actually had her killed.
The Duke finds that the Duchess is more pleasing in art as she does not disrespect him and reflects well on him and he can easily control her. The Duke imagines that she never appreciated her position as his wife and was possibly unfaithful, although there is no evidence for this.