This is where it's at, to me. Stepping into another skin for a while, and making the audience believe it's real. While part of my mind considers the characters and their reactions from an intellectual standpoint, there's also a part that registers the emotions they would logically experience, given their background and who they are.
For example, I finished up a short story not long ago that I had to do a lot of analyzing and thinking over in order to write it, but when I got to a certain point in the narrative, what the character was experiencing was so overwhelming that I sat writing with tears pouring down my face, because at that moment I was tapping into a universal depth of grief that most of us will know at some point in our lives. I had hit something powerful, and it moved me. It came through in the writing, too: the first reader to get that story cried reading it.
The corollary, though, is that like an actor, the author is the interpreter of the character's emotion. And that means the need to translate on the stage, while always being a little conscious of how the audience is perceiving the play. In other words, it's never about your personal emotions, or your bad day or good day when you're writing. It's about showing up at the set, ready to put everything into your job and give 100% to the illusion of reality you're going to create.
