This poem opens with a literally impossible declaration—that the speaker is “Nobody.” This nobody-ness, however, quickly comes to mean that she is outside of the public sphere; perhaps, here Dickinson is touching on her own failure to become a published poet, and thus the fact that to most of society, she is “Nobody.”
I am nobody!
Get outa here Nobody!
The speaker does not seem bitter about this—instead she asks the reader, playfully, “Who are you?,” and offers us a chance to be in cahoots with her (“Are you – Nobody – Too?”). In the next line, she assumes that the answer to this question is yes, and so unites herself with the reader (“Then there’s a pair of us!”), and her use of exclamation points shows that she is very happy to be a part of this failed couple.