The poem is a dramatic monologue written by R. Brownie, that introduced this form of poetry. 

Reading the title, the intelligent reader, focus his attention on the word "last" that produces curiosity in the reader indeed he can may wonder why the duchess is "last". At the same time, also the word "my" and the setting produce curiosity in the reader. 

According to the dramatic monologue, the speaking voice is a first person narrator, in particular a duke. He is speaking to a messenger, that is a stranger, and he never answer the duke. The duke is speaking about a fresco of a girl (and reading the poem the intelligent reader understand that the girl is the duchess) that is dead. 

Reading the monologue, the reader understand that the duke has never shown the fresco to anyone untill that monologue. He also receives other informations reading the poem step by step. In particular the reader know the personality of the duke: he has a patronizing, possessive, selfcentred and jelous attitude indeed only the duke chooses people who can see the fresco. 

The monologue delineates the obsession that the duke has got for "his" duchess. He is extremely jealous and he doesn't bear that his wife gives attentions to other people. 

An other information that Brownie indirecly gives to the reader is that the duke brings to the death of the duchess.