When a player (generally the quarterback) changes the play call at the line of scrimmage.
Most plays are called while all players are in a huddle; the quarterback would 'audible' if he didn't like the original play call based on what formation he saw the defense in or if there were an opportunity that could be exploited.
Most play calls are sent to the quarterback through a headset in the player's helmet or signs from a coach on the sideline.
Peyton Manning is one of the most famous quarterbacks for audibling plays at the line of scrimmage. He keeps defenses on their toes by changing the play based on what he thinks the defense is setup to do. Manning notoriously waves his arms and yells, to the point that defenses must guess whether or not he's actually calling an audible.