That's a great definition. I think we can all objectively agree on that definition, but that doesn't necessarily mean that the thing being described by the definition is any less subjective.
Actually I think it's quite possibly the worst definition of consciousness I've ever seen.
At best (assuming conscious cannot be doubted) it's like saying "Cars are those things which move fast". In the sense that it describes one property of cars, or consciousness, but not a unique property. Other things move fast, not just cars, other things could be beyond doubt than just consciousness.
At worst (assuming consciousness can be doubted) it's like saying "Cars are those things which flap around", which is utterly nonsense, and unhelpful. Plenty of things "flap around", but cars don't...
My point is, if you don't already have a strong preconception of what "consciousness" is, that definition is worse than no definition at all.