Believability - I don't think it's a word, but it should be.
All acting stems from this. I don't care what history work you did, and that you're mother in the scene is an alcoholic, and your dog just died. None of it matters if I don't believe you.
The reason all those acting greats are so great? You fucking believe them. Think of Roy Scheider in Jaws. Remember the scene? When Jaws comes up out of the water, while he's throwing chum out to sea. His look is completely blank. You totally believe he just saw the biggest fucking shark he's ever seen, then he says, "We're gonna need a bigger boat." and you are completely there, you totally buy in. You believe him.
Every other lesson, task, motivation, whatever it is you're doing to make the scene feel more "alive," should stem from this one thing. Am I believable?