"The Brain—is wider than the Sky—" is all about the human brain. Which, you know, figures. The speaker is basically saying that our ability to imagine and accumulate new knowledge is the best thing ever. Though our brains are only about the size of a small rotisserie chicken, they have the ability to dream of the infinite and to constantly accumulate new knowledge. No wonder Dickinson was so inspired.
The poem celebrates the ability of the human mind both to absorb information and imagine new things.
The speaker of the poem seems blind to fact that there might be things outside of our realm of comprehension.
Nature is a major theme in many of Dickinson's poems, and "The Brain—is wider than the Sky—" is no exception. We get references to the wide-open sky, the deep blue sea, and God, who the speaker seems to consider nature itself. The interesting thing with this poem, though, is that the speaker thinks that man is cooler than all this nature stuff.
The speaker of the poem places the power of humanity's intellect above the power of nature, which is straight-up ridiculous.
Ultimately, the speaker says that our brains give us the power to be at one with God, which the speaker considers to be the raw power of nature itself.
Though it's widely known that Emily Dickinson didn't exactly jive with the Christian powers-that-be of her day, it's also known that she considered herself a spiritual person. In poem after poem, we find spiritual themes. Sometimes they seem like angry rebellions against the religious status quo, but there's a lot of mellower soul searching involved as well. Though "The Brain—is wider than the Sky—" has some ideas that might set off alarm bells for some religious people, there's a definite spiritual feeling about the poem as the speaker tries to reconcile all the stuff inside her brain with the infinite universe around her.
The speaker has a contentious relationship with God and values the human intellect over spirituality.
The speaker expresses the belief that the human intellect is itself divine and is the very thing that connects us with the spiritual world.