This question refers to the concept of an American "frontier" as understood by Frederick Jackson Turner and Patricia Limerick. Turner was a late-nineteenth and early-twentieth century historian whose 1893 essay "The Significance of the Frontier in American History" is generally regarded as a seminal work in American historiography.
In it, Turner argues that the source of what he regards as a unique American identity can be found in the frontier, which is more of a concept than a place. Throughout American history, he argues, "civilized" Americans moved west, where they formed a sort of leading edge of civilization. As they did so, they were forced to "rebuild" civilization, thus creating a place where American democracy was rejuvenated. Thus, he argues that the frontier is "the line of most rapid Americanization": a space where all of the things Turner understands to be unique to the American identity—individualism, democracy, and social equality—are present and constantly being reinvented.
Turner's essay, delivered to the American Historical Association in 1893, was written in response to the "closing" of the frontier in the wake of the 1890 census, which revealed that the West had essentially been entirely settled by whites.
Patricia Limerick is a modern American historian whose 1987 book Legacy of Conquest was important in ushering in a new way of understanding the West. Like many modern scholars, Limerick repudiates Turner's rather romanticized view of the frontier and the West in general. Rather than a place where democracy was rejuvenated, she writes, the emphasis should be on the conquest and expropriation of Native Americans and the Mexicans, whose lands were taken by conquest. Turner described the western frontier as "free land" and did not take the perspective of its indigenous (nor Mexican) inhabitants into account.
Limerick also looks at the people who actually settled in the West, including Asian American immigrants, who consistently faced discrimination and persecution. Turner worried about large corporations, including railroads, gobbling up Western territories, and Limerick also points to corporate interests, backed by the federal government, as the real force in westward expansion, far more than the hardy pioneers lionized by Turner. In short, where Turner viewed the frontier as a process where American democracy was renewed and revitalized, Limerick regards it as a place conquered by the United States, a colonial power.
In the introduction to Legacy of Conquest, where she compellingly compares the conquest of the West to the practice of slavery in the United States, Limerick writes that Turner's view of frontier history (as well as those of his many students and adherents among historians) is "at base a judgment of sentiment and nostalgia," and she chooses to frame Western history as the "study of a place undergoing conquest and never fully escaping its consequences."
While both historians see some continuity in the West (Turner's ever-cycling frontier and Limerick's notion of the West as a colonized place), Limerick rejects the idea that the frontier "closed" in 1890. This can only be true if one imagines the West in romanticized terms like Turner's. The days of rugged pioneers bringing a rough form of democracy to the wilderness never really existed to begin with.