New Criticism is a critical theory which essentially denounces the importance of the historical or societal matters (from the period it was written) surrounding a text. Instead, the movement focuses upon the text alone. New Criticism asks those who analyze a text to conduct close readings of a piece in order to define what it is really saying.
For the most part, I would suggest that New Criticism is only partly successful. As a teacher, I find author intent and the historical significance of a piece important. That said, my students also examine a text through Reader-Response and New Criticism methodology.
Think about it this way: a text exists in two very different lights--the one the author created it in and the one it exists in today (apart from its place in history). Therefore, a text must be read in different ways. While what the author wanted of readers is important, what readers want of the text is more important. It is only through a close reading that a reader will deeply engage with a text.