The Resonance Battery is a special that provides boosts to combat speed, damage, and defense to a ship if that ship is currently being affected by a Tactical Module.
In order for the Resonance Battery to have an effect, the ship it's on must be affected by the Tactical Module aura it's within. For example, if your ship is currently being slowed down by an enemy Engine Disruptor, that ship will receive all the bonuses listed above. However, if your ship is inside your own Microwave Dampener field, it will not receive the above bonuses because Microwave Dampeners only affect enemy ships and buildings.
In essence, any ship with the Resonance Battery will gain from its bonuses when that particular ship is being affected by either a hostile aura, or a friendly one. So if a ship with Resonance Battery is having its turn speed increased by a friendly Navigation Array aura, the Resonance Battery's bonuses will apply. It's also important to note that a Destroyer ECM's built in tac mod activates the Resonance Battery.
This effect does stack; for each Tactical Module aura affecting your ship, the bonuses increase. However, the bonuses are multiplicative, meaning each additional bonus contributes less each time. The bonuses also affect any type of incoming or outgoing damage, including concussive and radioactive.
The Resonance Battery only provides boosts to the ship on which it is equipped.