I think they mean conscious as in "to be conscious of", for example: I exited my house while daydreaming/thinking about other things, so I was not "conscious of" the fact that I did not bring my keys with me aka I did not have awareness or was not operating in the moment/mindfully because my mind was elsewhere
I think they're attempting to describe the difference between being present/aware of every moment we experience, vs. a habitual 'autopilot state' that we can find ourselves in (the phenomena of driving somewhere and then not even remembering the drive there, for instance) where we're really not aware of what's going on in our lives, because the mundane things are so habitual that we don't even need to be fully aware of what we're doing to do it - but that alternatively, choosing and teaching ourselves to be aware at all times, even during our mundane, habitual routines, is potentially a better way to exist