Most people are not comfortable performing in front people. When I say of performing, such as an instrument, or singing, or acting, I mean more than just knowing how to do well at your chosen craft, I mean doing it well and in front of people. Its the standing in front of people part that gets us every time. How many of us sing like a bird in the shower but then when people are watching we cannot carry a note. Here are three steps to start you on the road to comfort (never complete) when called on to shine.
1. Don't neglect to practice. Whether you sing or play an instrument practice is the key to being relaxed. The more familiar you are with what you are performing, the less anxiety you will have about messing up.
2. Don't back up. Piano teaches pass this on all the time. If you mess up in the middle, or any place in your piece, don't back up and repeat the offending passage. Keep going. Chances are your audience didn't even notice.
3. Try not to be critical of your technical skill. Focus more on your overall performance. How does it sound as a whole? If you're a pianist and you worry during your piece about your fingering then you're ignoring the song and how it sounds. Worry about technicalities when you practice. Which should be often.
With time playing in front of and for other people will come much easier. You'll be a natural. So use every opportunity to show your stuff!