If nothing can faze you, you are unflappable. Nothing bothers you, or gets you off your game. To faze is to disrupt or disturb.
Faze is a new word, descending from a word that meant to frighten away. At basketball games, when a player is shooting a foul shot, fans behind the net will try to faze the player by waving towels and making loud noise. They are trying to disturb him, so that he misses the kind of shot he's made thousands of times before.