Mighty bonus is an item property for bows. It allows the user of the weapon to add a damage bonus equal to his or her strength modifier or the mighty bonus, whichever is the lower. This bonus is similar to the damage bonus applied to melee weapons for having a strength greater than 11.
NWN & 3.5 Rules Comparison
In the Pen & Paper version of Dungeons and Dragons, a user of a bow with mighty bonus would receive a attack bonus penalty equal to the difference between the mighty bonus and the strength modifier, if he or she did not have a strength modifier equal to or greater than the mighty bonus.
This was not the case in NwN1 and possibly not the case on NwN2 either.