Definitions for fair catch
Random House Webster's College Dictionary
a catch of a kicked football made after the receiving team signals that it will not attempt to advance the ball.
Origin of fair catch:
(American football) a catch of a punt on the fly by a defensive player who has signalled that he will not run and so should not be tackled
A call on a kicking play in which the receiver waves his hand to indicate that he will not run with the ball, assuring that he will not be tackled after catching it.