Intelligence
Dragons are very intelligent creatures - at times seeming to approach human levels of intelligence and emotion - but they never specifically display it: Dragons can't physically talk, and although they can understand voice commands from humans, this is no more than what a dog or a horse can do. Rather, dragons appear to have some sort of higher, unnatural level of intelligence; they seem to be more in tune with "magic" (or "fate" or "nature") than humans are, and possess a sense of mental awareness that humans do not. Somehow, they are often able to sense when the human rider they are bonded with needs them (something hinted at in the Season 5 episode "The Dance of Dragons", when Drogon arrives seemingly out of the blue to rescue Daenerys). Historians in Westeros have frequently lamented that men could never truly understand the mind of a dragon, and that sometimes dragons took certain actions for inscrutable reasons.