As an actor, I can say it has something to do with physicality. Each character has a different walk, a different carriage. I work to find where in my body each character lives, and that knowledge informs the performance.
There is also knowing more than the mere plot. It’s knowing what happened before and what comes after the events of the play or the movie. In some cases, I’ve gone as far as writing a life story of the person I’m portraying.
Most modern actors leave me cold. There are a few performances I’ve seen that were heart-wrenchingly authentic. Colin Firth in The King’s Speech was one. It wasn’t simply his recreation of the stutter. It was his embodiment of character, the person. It was inspiring.
One often hears an actor talking about motivation in a scene, the “why” of the events. The actor has to know his/her objectives, both major and minor ones. A character’s desires are important. How an actor relays these to the audience must be nuanced and well thought out.
In my opinion, brilliant actors aren’t born. They’re trained. They study the craft of acting. They learn about their own foibles and face them unflinchingly and hopefully overcome them.