The Fellowship of the Ring is set in Middle-Earth. In Tolkien's writings, Middle-Earth is a continent in the center of the Earth (which is also referred to as Arda), in a fictional period of the past. Middle-Earth roughly corresponds to Europe and The Shire, where most hobbits live, is roughly analogous to England.
Middle-Earth is populated with a number of fantasy creatures, including hobbits, dwarves, elves, wraiths, orcs, and trolls, as well as humans. A distinct aspect of Tolkien's depiction of Middle-Earth is its extensive fictional history and mythology, a technique called "mythopoeia" (or myth-making). Tolkien often presents brief references to this fictional past in order to create the impression of a vast history in Middle-Earth, such as when Aragorn (still, at this point in the novel, known as Strider) describes Weathertop to the hobbits when he guides them out of the human-hobbit town of Bree:
The Men of the West did not live here; though in their latter days they defended the hills for a while against the evil that came out of Angmar [...] But long before, in the first days of the North Kingdom, they built a great watch-tower on Weathertop, Amon Sûl they called it. It was burned and broken, and nothing remains of it now but a tumbled ring, like a rough crown on the old hill’s head. Yet once it was tall and fair. It is told that Elendil stood there watching for the coming of Gil-galad [...]
When Merry asks who built the ancient path they walk on, Aragorn provides a brief glimpse into the ancient history of Middle-Earth, noting that men of the "North Kingdom" built a "great watch-tower" on Weathertop, which they knew by the name "Amon Sûl," in order to hold the line of battle against "the evil that came out of Angmar." Here, then, he provides a brief fragment of an ancient history unknown to the hobbits, detailing the conflicts of kingdoms that have long since ceased to exist. Though this history does not directly concern the hobbits or their journeys, it helps to create the impression that Middle-Earth is a setting with its own long history of conflicts and heroes, as well as a number of different cultures and languages that have developed over time.