The protagonist of this story is young Sylvia, a girl of nine who much prefers the company of animals to people. She used to live in the city but could not thrive there; however, she seems to have come to life when she moved to her grandmother's farm in the country. In many ways, then, she is associated with nature, as even her name -- Sylvia -- comes from the word sylvan, which means associated with the woods or the pastoral.
The antagonist of the story is the urban desire to tame and possess nature, as represented by the hunter. The fact that he is nameless is a good clue that he is representative of something larger than himself: he symbolizes the desire of many urbanites to conquer the country, to exploit its resources for manufacturing, or fashion, or personal use (such as taxidermy).
The conflict, thus, exists between character (Sylvia) and society (as represented by the hunter). The hunter himself, in isolation, would not be a terribly crucial problem, but his symbolism of industrialization, of the exploitation of nature for its resources, is the much greater issue. The danger that modernity posed to nature during this era (the story came out in 1886) was, perhaps, not spoken of enough. Jewett's story attempts to draw attention to the dangers -- not just to nature, but to humanity -- of the need to conquer and control the pastoral.