A person who introduces performers at a concert or show is called?

An MC or Master of Ceremonies.

If it's a variety show, we call him the "MC," or "Master of Ceremonies."

Then you have the "Game Show Host," and the circus "Ring Master."

I don't know of a special name for an announcer at a concert.
The guy who tells you to turn off your cell phones?

For the concerts I attend, the conductor walks on stage and everybody claps.

A compere could be the person you are referring to.

compère— a new word for me, thanks!