Strength increases damage done by weapons with a scaling mechanic. A letter denoting a weapons specific scaling properties is noted beneath the weapon's required strength stat. The letters range in order of effectiveness from E, D, C, B, A, and S.
Weapons with an E rating for scaling will receive a poor benefit from investment in strength while weapons with an S rating receive the greatest benefit.
As is with every other stat in the game, it also has indirect bonuses such as increasing the player characters flat damage absorption.