New Historicism was codified and named by Stephen Greenblatt, writer, editor, and former president of the Modern Language Association. It has ties to Marxist criticism of literature but considers itself separate in key details.
New Historicism is simply the desire to explore and research history through the eyes of literature with the understanding that one's own subjective experiences and biases make objectivity an unreachable goal. Instead, scholars of New Historicism attempt to relive a work through the time of the person who created it, taking into account norms, ideals, prejudices, and any other subjective experiences that a person of the time would hold. This goal is itself impossible, because a modern scholar is of his own time just as a Renaissance man is of his, and so cannot hope to truly understand the time and culture that produced a work of literature.
Therefore, to study a work, one must use it and all other available information about the era to reproduce the artist's ideology, and thus gain a small understanding of the massive, unknowable past culture that produced the work.