New Criticism is generally concerned with finding the intrinsic worth of litearture. It focuses on "the work of art as an object in itself" and it uses different language than those science (Harmon and Holman 337).
It grew from American and English writers in the 1930s, including T.S. Elliot and Ezra pound, and was pushed forward by critics John Ranson and William Empson.
New Criticism has a hard time defining itself, except in declaring what it isn't. It is not traditional and it does not allow for talking about art in "general terms not directly relating to the artwork itself" (Harmon and Holman 337).
New Criticism focuses often image, symbol, and meaning over all other aspects of writing including genre and form. Typically this approach works best with verse over prose writing as New Criticism falls short when applied to longer fiction or drama.
New Criticism emerged in the 1930s, most identified with an English journal called Scrutiny. New Criticism was, in part, a reaction against the historical criticism of the time, which was considered sometimes to be too speculative, positing for example, that Emily Bronte must have had a lover like Heathcliff to be able to write Wuthering Heights. Instead of these kinds of speculations, the New Critics focused narrowly on the texts of great works. They did close readings of the symbols, metaphors, irony, narration and other parts of the text, as well as looking at characterization, setting and thematic elements. According to Terry Eagleton in Literary Theory, New Criticism arose as well in reaction to source criticism, a form of criticism that looked at the often Greek and Latin sources of literary works. By the turn of the twentieth century, many of the people coming out of the new working class universities had never learned Greek or Latin and needed a different context for studying texts. New Critical Criticism filled the void. In any case, New Criticism is the bread and butter of how we generally all learned to read texts in high school.
New Criticism also focused on finding unities in texts. This form of criticism was dominant through the 1970s, at which point post structuralist thought swept through university English departments.