How exactly does the audience get it?

 Years ago I had a hot debate with a fellow performer.  We had both noticed that in some performances, the performers were able to create strong emotions in the audience.  Sometimes, under the right circumstances, the appearance of sadness in the performer would make the audience cry.  The performer's joy could make the audience joyful.  He was trying to convince me it was magic, as in "could not be explained by science."  That rubbed me the wrong way, so I argued that it had to be something to do with what the performer actually did, and what images and sounds made their way from the performer to the eyes and ears of the people watching.  But the actual mechanism remained a mystery.

The act of feeling what someone else feels is of course known as empathy.  Enter Jeremy Rifkin, who wrote a book called The Empathic Civilization.  If you don't have time to read the whole book (I haven't yet), this ted video seems to be a pretty great summary.

Basically, the answer is something called "mirror neurons" - we're wired up to fire the same neurons whether we are performing an action ourselves, or just watching someone else perform the action.  It's just like our reality and our dreams, which at some level in the brain can not be distinguished from one another.  So when we watch performers have an experience, we have it too.