It's well defined in the philosophical literature as the felt experience of colors, sounds, pains, etc which make up our subjective experiences of perception, imagination, dreams, etc, Qualia is the technical word, but it's also controversial, depending on the philosopher's position on the hard problem and their views on perception (they might replace qualia with representational or relational properties).
Another way of putting it is to use the primary versus secondary qualities. Primary qualities belong to properties of things we perceive. Secondary are properties that are part of the perceiving or experiencing subject. Shape, number, composition are properties of things. Sounds, colors, pains are properties of a perceiver.
Well-defined in the philosophical sense, perhaps (though I think some would disagree). It is not well-defined in the scientific sense. There is no way to quantify or classify something as conscious.
Another way of putting it is to use the primary versus secondary qualities. Primary qualities belong to properties of things we perceive. Secondary are properties that are part of the perceiving or experiencing subject. Shape, number, composition are properties of things. Sounds, colors, pains are properties of a perceiver.