Normally when one of your creatures attack your opponent and are unblocked, they break a single shield regardless of their power. Each of these keywords allow your creatures to break additional shields (except Master Breaker). While Breaker abilities are effective in increasing a creature's offensive presence, it does increase the risk of activating Shield Triggers which may cause reversal. It doesn't affect the battle zone directly as well, so creatures with only a breaker ability should be avoided.
World breaker(This creature breaks all your opponent's shields.)
Each of these abilities break a specified amount of shields.
The majority of creatures have a power divisible by 6000 for each additional shield they break.
A 6000+ power creature would have Double Breaker, a 12000+ power creature has Triple Breaker, 18000 power creature has Quattro Breaker and a 24000 power creature has World Breaker.
Powered Breaker(This creature breaks an additional shield for each 6000 power.)
The abilities of these creatures are affected by other aspects of the game state such as cards in your battle zone, mana zone, or for the total power of the creature.
Master Double Breaker(This creature breaks 2 shields. During the turn this creature is put into the battle zone, before each break, destroy one of your opponent's creatures.)
Dragon Double breaker(This creature breaks 2 shields. Before each break, add the top card of your deck to your shields face down or on top on one of your shields face up.)
Dragon Triple breaker(This creature breaks 3 shields. Before each break, add the top card of your deck to your shields face down or on top on one of your shields face up.)
In addition to breaking your opponents shields, they trigger another ability.
Next Breaker(Whenever this creature would break a shield that doesn't have a face up card, your opponent turns all cards on that shield face up instead.)
If a creature has multiple 'Breaker' keywords such as Double Breaker and Triple Breaker, you must choose one. From that example, you can choose to break 2 or 3 shields (but not 4 or more).
Choosing which Breaker keyword breaks shields is chosen at the time after the 'block processing' step at the 'broken shield' step. Even if you don't have a Breaker ability at the 'declare attackers' step, if the creature gets a 'Breaker' ability during the attack, the creature will break additional shields.
If a creature has a 'Breaker' ability, they must break that many shields. If the creature had Double Breaker, they must break 2 of their opponents shields when they break.
When your opponent has no shields and one of your creatures attacks them directly, you win the game. Creatures with a "Breaker" ability break more than one shield when they attack your opponent. If your opponent has fewer shields than your attacking creature can break, your creature doesn't defeat your opponent, just however many shields are left.
If multiple shields are broken in a single attack, they are broken at the same time. See March 25, 2017 Rules revision.