That means you don't get any + power increases either by bonus or ability. However, if you copy an all star card power, or any card with - power abilities, your copied power will get deducted by the opponents bonus/ability
Ok here's how it works.
Power = Opp Power means that your card will copy your opponent's base power, so let's say you use a power = power opp card on Trish, you get 5 power technically. But because of Trish's power-reduction, your power gets dropped to 5 - 3 = 2. This goes the same for All-Stars for example, Slopsh against Karen will give you 5 power.
Reduced by your own bonus? I assume you're playing All Stars? There could be a chance you're facing an opponent with Copy: Opponent bonus. If that isn't the case, can you describe your case in detail?