In battle
Aura Break inverts the effects of Fairy Aura and Dark Aura: instead of multiplying the power of Fairy- or Dark-type moves by those Abilities' normal multiplier of 1.33, the power of moves of that type is divided by 1.33 instead, resulting in approximately a 25% decrease in power as long as both Abilities are active.
Even if a Pokémon with Mold Breaker, Teravolt, or Turboblaze uses a Fairy- or Dark-type move, the effect of Aura Break still applies.
Outside of battle
Though Aura is one of Zygarde's possible abilities, the game treats Zygarde with this ability as a different form to a Zygarde with Power Construct, with both forms only having a single possible ability and thus preventing the use of an Ability Capsule to switch between Aura Break and Power Construct.