What I notice in actors/actresses is when there's some little thing(s) they do that makes me think, "This person really knows how a person saying/doing that particular thing would be (or what s/he's do). There are subtle things (facial expressions, subtle body language) people do in real life, and only someone who is familiar with those things (or someone so in tune with some situations/feelings that he'd be able to imagine himself in a situation and use subtle facial expressions/body language as if it was real).
Sometimes the best acting can show up in the least dramatic parts of a performance. Sometimes, too, the more dramatic a part of a performance is, it is the best actors/actresses who know how not to "do the standard thing" associated with emotions and who, instead, do the thing only someone very tuned into what people do in real life would know to do.
I'd compare it to the way comedians often strike a chord with the audience by saying something the audience hasn't actually thought on their own, but once it's said by the comedian it strikes a chord. Some comedians strike a chord when they say what we were also thinking but may not have said. Others can strike a chord when they say what we didn't realize we were thinking until they said it and made us realize it.
I think it's the same with those subtle things the best actors/actresses know how to do. Although I certainly see a lot of good acting among the Academy Award winners; some of the best acting I've seen has sometimes actually been in something like commercials or something like bit parts in some fairly "unlofty" television shows.