To put in perspective, Beam arrays give -10 to weapon power when fired in succession.
It just means that sustained weapons fire lowers your weapon system power over time. The lower the power, the less damage your weapons do.
At 100 power weapons deal double the listed damage
At 50 weapons deal the listed damage
At 25 weapons deal half the listed damage
Turret boats are fun to use in PvE, and the animations are pretty neat (It feels great to always have all your weapons firing all the time) but unless you are running full power to weapons, using Emergency power to Weapons BOFF abilities, or eating batteries, your Damage will drop off rather quickly.
As Owen said, it applies to your power level, but only when firing (the quad phaser cannons with -10 to engine power are also only during fire).
If you have a high EPS transfer, it shouldn't be very noticable. I run a Dread with the quad phaser cannon and the breen set in addition to 6 points in EPS transfer and my transfer is something like 12.4 recovery per second (so I can fire quite a few weapons at once and they be at full power by the time the cooldown has recharged).