Whitman focuses on this theme about as directly as he can. The first five lines are all about nature. He uses the spider as an example of how things work in the natural world. The second five lines are all about human life and emotions, and how they might compare to nature. By the end, the two worlds are tied together by this metaphor, and they become hard to pull apart.
This poem isn’t really about nature at all, except as an excuse to talk about spirituality.