Through the use of symbols, the Duke reveals himself to be a man who desires total and complete power and submission from those around him. This desire for power and control is symbolized in the picture of his wife, which he keeps behind a curtain, and "none puts by the curtain" or draws it open, unless it is he, himself. His wife was a bit too out-of-control while she was alive. Her being represented by a still painting, hidden behind a curtain, that only he opens or closes, is more fitting for his control-hungry nature. This desire for total submission is again seen at the end when the duke points out sculpture of "Neptune...taming a sea-horse" that he had a sculptor "cast in bronze" for him. He picked an image of a great God taming a wild and rare creature-definitely symbolic of the duke's own egotistical image of himself as a God, and his desire to tame the rare beauties that are his wives. He even had it cast in bronze, a strong metal that secures its permanence and trapped figure.
The duke also uses imagery to describe his first wife's blushing, smiling countenance. There is nothing else in the poem, or in his description, that has quite such imagery and detail, as when he describes how flirtatious and easy-to-please she was. This ornate imagery that the duke uses to describe her smiles betrays how passionately he felt about it. He exaggerates her flirtatious nature, in order to make his case for killing her more sound. He states her smile, glance and blush as having "depth and passion", as being "a spot of joy," as a "faint half-blush that dies along her throat." He spends quite a bit of time describing her blushing happiness in the face of anything that was the least bit pleasing to her. Again, that use of imagery betrays his intense feeling about the matter, and how angry it made him. The rest of the poem doesn't have such detail; in fact, in describing his awful murder, all he says, and quite dispassionately, is "I gave commands."
Those are a couple ways that the duke reveals his character-through symbols and through imagery. I hope it helps!