The 50th anniversary of the Wilderness Act is Sept 3. The word wilderness did not show up much in the press or conversation until the 1960s and 70s. It is tossed around a lot now by people have never been to one.
Under the Act, wilderness is a place where "the influence of man is essentially unnoticeable", and "where there are opportunities for solitude." It takes several pages for the definition. Wilderness areas are supposed to be larger than 5,000 acres, but some in the East are smaller. The term is defined by an Act of Congress signed by L Johnson in 1964.
A wilderness area is designated Federal Land administered by the Forest Service, BLM, National Park Service, or the US Fish and Wildlife Service. There were some designated primitive areas like the Gila in New Mexico prior to the Wilderness Act. Most but not necessarily all primitive areas have been designated as wilderness. There are more and more wilderness areas all the time in Nevada. They burn the old buildings and close the old roads. It can be good or bad depending on your point of view.
The best practical definition for a wilderness area is anywhere more than 5 miles from the nearest dirt road. In Wyoming I have been 50 miles from the nearest dirt road, but in Alaska more like 80 or 100 miles.