Thirteen Ways of Looking at a Blackbird (title)
The title asks you to consider that you don't really know what a blackbird is until you've considered it from different angles. And even then you still only have a limited view of it. There is no one "real" or "true" blackbird.
I was of three minds, Like a tree In which there are three blackbirds. (Section II)
Stevens turns the blackbird into an element in a simile. How is a blackbird like a "mind"? At this point, it's good to remember what Stevens himself said about the poems, "This group of poems is not meant to be a collection of epigrams or of ideas, but of sensations" (source). So, what does a blackbird in your mind feel like?
A man and a woman and a blackbird Are one. (Section IV)
The speaker seems to be saying, "When you think about it, we're all just slices of the same pie. You, me, that blackbird over there…"