Short answers, pulled from the story.
Conceptual art, also called conceptualism, is art in which the concept or idea is prioritized equally to or more than traditional aesthetic, technical, and material concerns. Some works can be constructed by anyone simply by following a set of written instructions.
Henry Flynt coined the term concept art in 1961, in an article of the same name in the proto-Fluxus publication An Anthology of Chance Operations. He said it devolved from his notion of cognitive nihilism.
Sol LeWitt said the idea or concept is the most important aspect of the work, with all planning and decisions made beforehand and execution a perfunctory affair. He wrote that the idea becomes a machine that makes the art.
Marcel Duchamp paved the way for the conceptualists with his readymades, including Fountain in 1917, a urinal signed R. Mutt and submitted to the Society of Independent Artists in New York. Joseph Kosuth later wrote that all art after Duchamp is conceptual in nature.
Conceptual art emerged during the 1960s in part as a reaction against the formalism articulated by New York critic Clement Greenberg, who held that Modern art should reduce each medium to its essential formal nature. Some artists saw conceptual art as a radical break with his formalist Modernism.
Neo-conceptual art describes practices from the 1980s and especially the 1990s that derive from the conceptual art movement of the 1960s and 1970s. It includes the Moscow Conceptualists, United States neo-conceptualists such as Sherrie Levine, and the Young British Artists, notably Damien Hirst and Tracey Emin.