It is the act of putting one of your opponents shields into his hand when one of your creatures in the battle zoneattacks your opponent and isn't blocked.
If there is no creature with the Blocker keyword to stop the attack, one of your opponent's shields is broken. That means you get to choose one of those shields and your opponent puts it into his/her hand (unless an effect like Bolmeteus Steel Dragon's says otherwise). It also enables the opponent to use cards with the Shield Trigger ability, so attacking recklessly may cause ambush and reversal.
Break is referenced on Breaker abilities signifying how many shields a creature with the ability will break when they attack your opponent, as well as to trigger the conditions of Turbo Rush.