In "Birches," Frost incorporates ideas from two similar traditions. The first is the Romantic tradition, poets like Wordsworth, Coleridge, and Keats often set their characters in Nature (notice the capital N). The character (often male) would embark on adventures or long walks. Sometimes Nature would challenge him. Other times he would have blissful moments and feel one with the natural world. Sometimes these interactions with Nature got scary, but the combination of fear and joy made the character worthy of doing great things. The other tradition is the Transcendentalist tradition. Writers like Emerson, Thoreau, and Whitman toned down the scary part of Nature and almost made Nature into a philosophy/religion. This tradition became popular as American's started to explore what was left of America to explore. This exploration demanded a lot of labor and sacrifice, so people talked up the idea that it was America's destiny to recruit rugged individuals to live in the middle of nowhere. In this poem Frost plays around with many of these ideas.
"Birches" is about the masculine need to dominate the world, because the boy conquers trees while the girls are represented by conquered trees.
The boy has attempted to conquer trees and see heaven, but the man failed to conquer earthly life.