Conscious is an adjective that simply means alert and awake. If you fall from a tree and smack your head on the side of the wheelbarrow, there's a good chance you won't be conscious afterward.
Conscious is a Latin word whose original meaning was “knowing" or "aware.” So a conscious person has an awareness of her environment and her own existence and thoughts. If you're "self-conscious," you're overly aware and even embarrassed by how you think you look or act. But that sounds better than being unconscious, or totally unaware and out of it.