Subjective experience of the world around us. The one thing I'm 100% sure I do have, and it would require very special pleading (or solipsism) to insist other humans are anything other than almost certain to share that trait. My suspicion is that there is some threshold of cerebral complexity required for it to occur, and is pretty unlikely to apply to all animals with central nervous systems. Whether insect brains are sufficiently complex I really couldn't say, nor am I sure what test could be done to determine it (though one day we may have enough understanding to do such a test).

Information complexity is a physical quantity and we have many well-established methods of measuring it.