The Duke is trying to convey to the listener, who has come to broker a new marriage for the Duke, that his deceased wife was disloyal to him. He blames her for not bestowing her love, affection, and even smiles and blushes exclusively on him. As they are looking at a portrait of the late Duchess, he says to his listener:

He implies she would have been unfaithful because her affections were too far ranging. She liked everything and everybody equally to his mind: cherries from the bough, the sunset, her white mule, other men. The Duke condemns her for this.

She comes across as a sweet, innocent, affection young woman who loves the world around her and expresses her joy in it. As mention above, she loves cherries, her mule, and other people. She seems to like the Duke as well, for he says she smiles at him. She is a friendly, likable person who has a far kinder and less snobbish character than her husband. As the Duke himself says:

She had
A heart—how shall I say?— too soon made glad,
Too easily impressed; she liked whate’er
She looked on

However, as for the Duke, the impression the reader carries away is that he is a snobbish, controlling sociopath who saw his wife as an another object he had purchased, not a human being.