In boxing, a counter-hook is designed to catch an aggressive fighter coming forward.
This maneuver consists of a normal left/right hook, combined with some nifty footwork. As your opponent comes forward in an overly aggressive manner, you almost simultaneously take a step back, pivot on your lead leg, and swing your rear leg while throwing a hook.
The result is sort of like when a matador sidesteps a bull and sticks him, but instead you sidestep your opponent, and catch him with a hook for his efforts.
This punch is extremely hard to pull off in a boxing match, simply because it requires great footwork and a good amount of speed to land. A fighter must have the foot-speed to take a half-step back and pivot on his lead leg almost simultaneously.
A fighter must also have the reflexes to make his opponent miss, and the hand-speed to throw the hook while pivoting and swinging the rear leg. While any fighter can learn this technique, applying it in the ring requires much effort.
However, when used effectively, this can be a great tool to stop an aggressive opponent obsessed with bringing the fight to you. At the very least, if landed, this punch will throw your opponent off balance. If landed with authority, this can be a knockout blow, or at least a knockdown blow.
During an interview, Mayweather stated that he was taught the check hook in the Michigan amateurs.
Check Hook example: Mayweather Jr. vs. Ricky Hatton: Round 10