I once read a nice explanation of it: our physical reaction to the stress of performance comes from the body's "flight or flight" response to danger. The trick is to convince oneself there is no actual danger in the situation.
Yesterday I performed Jeux d'eau in a music salon with 15 or so attendees. I wasn't fully prepared- I hadn't played the piece in 12 years and attempted to bring it back in a few days, and it was a disaster. One of the most humiliating performances of my life. Wrong notes everywhere in places I thought I had mastered, doubts every other second, half-bars and whole bars skipped to save unsavable situations. But strangely enough, life went on. The sun went down and then up again this morning. People forgot it. Or maybe they didn't. But the session continued, there was good music that followed, I kept moderating, and I would like to think that it's about the music and not about me, that this one performance will not make people dismiss me or disrespect me forever. I apologized for the trainwreck (that killed no one) and recommended a good performance where people can listen to the "real" piece. True, this was no concert stage and the stakes were lower, but overall it was just a humbling reminder that it takes so much more to be able to share a piece with an audience, that if part of one thinks it can't be that easy, that one hasn't done enough preparation, then it's true. (I got so used to accompanying and playing from scores and forgot that performing demanding solo works requires a much more rigorous process).
One of my best friends in grad school was a wonderful pianist from Taiwan, and she always felt that there was something essentially narcissistic about being nervous. Getting nervous comes either from not being prepared or from the fear of making a bad impression, and performing is not about making an impression, she felt. You just have a message, and the more filled you are with the message you are there to share and with its importance, the less room there is for fear.