Radical Orthodoxy is a movement that seeks to use postmodernism as a catalyst for returning to an unapologetically Christian view of reality. In short, RO proponents criticize modernity's epistemology, ontology, and metaphysic - using many of the postmodern arguments put forth by thinkers like Lyotard, Derrida, and Baudrillard - and present a specifically Christian epistemology, ontology, and metaphysic.
RO orthodoxy seeks to break ties with all things "secular," since the very idea of a "secular" is really just a Christian heresy. There is no secular, neutral, objective lens through which to view life. Everyone is "biased." In short, every person interprets reality through a lens that, in large part, determines what he perceives about any person, place, or thing. Thus perception shapes reality. The question is not, Do you have a lens? but, What has influenced (i.e. "shaped") your lens?
Even secular thinkers who boast of rationality, scientific achievement, and empirical exactitude have been shaped by a lens that is rooted in a faith-narrative. Everyone must place their faith in a lens. Thus, RO places a high emphasis on how "presuppositions" shape the way a person thinks. For the Radically Orthodox thinker, God is not so much a conclusion at the end of a deductive argument, but the proto-supposition (a lens) through which all other "things" are seen, experienced, known. On this paradigm, Classical and Evidential apologetics feed into an intrinsically anti-Christian (secular) approach to the world - they must, therefore, be rejected.
What RO is pushing for is an approach to life that seeks to let God's self-revelation (through His Word, Church, Sacraments, community of children, and most importantly, His Son) shape us into the people He wants us to be, the people who see the world through the lens He has given us. Therefore, RO is intensely theological insofar as nothing (not politics, not sex, not money, not food, etc.) has any self-defining categories apart from God's revelation. To think about anything (literally anything) apart from God is to fail to see the world through the lens He has given us, and to participate in a pagan ontology. Nothing can be seen, known, and defined apart from God.
Smith's book provides a wonderful introduction into this dialogue. His perspective is refreshing, engaging, and challenging.