Before the advent of New Criticism in the 1930s, most literary criticism was either biography or source study. This meant that most literary critics and scholars were examining the lives of great writers or studying what works of literature influenced these writers. The text itself was often neglected.
The great achievement of New Criticism was putting the work of literature squarely at the center of study. A reader could approach any text without having to know anything about the life or literary intentions of the author. A reader also—and this helped the many working class people entering night schools—did not have to know much about Classical or other literary sources to interpret a text. The focus was on the text as text: what was the plot, the theme, the setting, and how were the characters portrayed? What was the narrative point of view: who was telling the story? What kind of formal devices, such as metaphor, simile, pun, irony, aphorism, or imagery was the writer using?
You may be saying to yourself, this is exactly how we study literature in my classroom: what is new about this? It is no longer new—it was new in the 1930s when it revolutionized literary studies. Now, indeed, it is the standard way we study a text, though supplemented by other critical approaches. However, it is still called New Criticism even though it is almost a century old, because that is what it was first called.
This method is also often called a "close reading" of the text, which means the scholar is paying very close attention to everything going on in a work of literature. Even Derrida, famous for rocking the boat with the introduction of deconstructive interpretations of texts, said his work was based fundamentally on close readings.