Browning's "My Last Dutchess" is a particularly well-done and tantalizing example of the dramatic monologue. The dramatic monologue reveals the essence of the single speaker as he or she has a "one-sided" conversation with a listener who remains silent throughout. We learn the subject of the dramatic monologue by implication, and, most important, the poet gives us significant insight into the character whose monologue we hear--insight sufficient to tell us whether we are listening to a trustworthy or untrustworthy person.
During the Duke of Ferrara's monologue, for example, we learn that the Dutchess was "too soon made glad, Too easily impressed." To us, she may seem like a delightful person, but to the Duke, she was, among other things, too liberal with her smiles and too quick to be happy. Of course, the power of the dramatic monologue is that we learn far more important things about the Duke than we do about the Dutchess. We learn that the Duke is angered the his Dutchess seemed not to weigh his "gift" of an old and honored name more heavily than some small kindness like a "bough of cherries" someone brought her from the orchard.
When we learn that the Duke, completely frustrated by her ready smiles, orders her to stop, we know that we are dealing with a man who has gone slightly over the edge of normal behavior--in other words, we are presented, in the Duke's own words, of a seriously jealous man. And when he says her smiles "stopped together," and no more mention is made of her, we are forced to conclude that perhaps the Duke stopped her smiles permanently. The Duke is completely silent on what happened, and this silence convicts him as much as an affirmative confession.
The dramatic monologue, especially in this poem, tells us everything we need to know about the speaker in order to form a moral judgment about him, and we come away from this monologue with the understanding that we have been listening to a jealous, vindictive, dangerous man.