Consciousness (n.) That part of the mind that thinks it is in charge, and convinces other minds that there is someone home, and the lights are on, while the rest of the mind gets on with the real work of doing everything.
"I think, therefore I am", is a circular analysis. One thinks one thinks, therefore one thinks one is. However that proves nothing except our ability to construct linguistic slipknots. Having defined existence as the ability to think leaves us with the issue of defining "think". What seems more accurate is "I think, therefore you think I am". And this is the key: our existence is defined not by our own minds but by other minds. Even our acts, if they are unseen by others, do not exist in any useful sense of the word. It is notable that our deliberate acts, though we believe them to be based on conscious decisions, register in our conscious mind several fractions of a second after they register in our subconscious, and in many cases, after we in fact execute them. The consciousness is left in the role of an observer, and above all, rationalizer of our acts towards others. The most accurate summary being: "I can explain! Therefore I am".