Big Integrity is the art and science of coming into right relationship with Reality and supporting others in doing the same. It can be spoken of as “getting right with God,” but religious language is not necessary and may in some circles be counterproductive, given the fact that so many people still have trivial, unnatural views of the divine. (Indeed, as I suggest here, atheist scientists such as PZ Myers and Richard Dawkins are playing traditionally prophetic roles in this process when they speak on behalf of reality.) Thus, I prefer thinking of Big Integrity simply as “being in right relationship with Reality”—both objective reality: the actual, physical Universe that dozens of scientific disciplines help us understand, and subjective reality: the inner realm of meaning, values, and interpretation that has historically been the focus of religion, psychology, and spirituality.
A nice post on the Big Integrity movement from Michael Dowd.