Describe/analyze the character of the lady (the Duchess) in "My Last Duchess"? What do you notice in her?
The former, now deceased, wife of the speaker in "My Last Duchess" was, in life, polite, respectful, friendly, and beautiful. She was, unfortunately for her, not a snob, which is what her husband wants in a wife.
In short, the Duchess in the poem now behaves like the Duke expects a wife to behave: like a work of art reflecting back on him. The poem begins and ends with the Duke displaying works of art. Notice the works of art are important to the Duke not for their inherent beauty, etc., but because of how they reflect on him. The final piece he points out, for instance, is valuable because it is rare and was created just for him.
The Duchess was respectful and appeared to be very nice to the Duke, but the Duke, according to his own words, was not the only source of her joy. She found pleasure in nature and people who would do small favors for her, etc. The Duke was not her only source of joy--therefore he ordered her to be killed.
The Duchess is in the present of the poem the ultimate trophy wife for the Duke.