Your Strength level determines your max hit in combat. Whenever you hit your opponent, you will deal a random amount of damage up to your max hit.
Most weapons have a Strength bonus that will also increase your max hit. You can view your Strength bonus (and all of your equipment's stats) by selecting 'View equipment stats' under the Worn Equipment side panel.
Congratulations! You are now a master of Strength. Why not visit [Sloane/Yadech Strongarm] at the Warriors' Guild? He has something special that is only available to true masters of the Strength skill!