When you title your poem, "Thirteen Ways of Looking at [Something]," you're describing versions of reality pretty much by definition. Indeed, "Thirteen Ways of Looking at a Blackbird" is not so much about a blackbird as it is about the different short takes that Stevens presents on the blackbird. It invites you to look at the world in highly specific, imaginative ways, like the circles of which the blackbird marks the edge. The imagination is the real star of the poem, and it has a way of creating its own reality. The number thirteen is completely arbitrary – Stevens seems to say that there are infinite versions of the blackbird rather than one, "true" blackbird.
The number "thirteen" is used because it is one more than the number of hours on a standard clock.
The poem's thirteen sections are deliberately fragmentary and incomplete.