Emerson famously says in this essay that in the woods he becomes a "transparent eyeball," or "part and particle of God," phrases which suggest a kind of dissolution of the self. Understanding Nature, for Emerson, requires solitude and "the heart of a child," a kind of egoless, open-hearted reception of reality. This condition is intrinsic to existence.
He writes that "every man's condition is a solution in hieroglyphic to those inquiries he would put," meaning that life, when properly considered, contains within it the answers to questions about the nature of existence and the inherent divinity of all things. These ideas have remained powerful to this day.
Emerson also anticipates modernism in his rejection of tradition and the old, classical ways of thinking about Nature. His initial question, "Why should not we also enjoy an original relation to the universe?" suggests that rather than relying on old forms ("the sepuchres of the fathers") we should come to know Nature directly, through our own lived experience. This notion that personal experience is more vital to humanity than tradition, and just as legitimate as an object of study, underlies much of modern thought.
While it would be inaccurate to say Emerson invented this idea, the notion of "seeing things for oneself," or personal observation, is both an expression of the American democratic ideal and a fundamental principle of science.