Conscious means "having an awareness of one's inner and outer worlds; mentally perceptive, awake, mindful."
So "conscious business" might mean, engaging in an occupation, work, or trade in a mindful, awake fashion. This implies, of course, that many people do not do so. In my experience, that is often the case. So I would definitely be in favor of conscious business; or conscious anything, for that matter.
Source: Foreword to The Spirit of Conscious Business, Fred Kofman
Contributed by: ~C4Chaos