Strength is a measure of the raw physical power of your character, determining how hard it can hit with melee attacks, how much weight it can carry, its base armor rating, its ability to intimidate other creatures and to break objects. It also grants a significant bonus to maximum life, and is used as a requirement to equip heavy armors and weapons.
Reaching a Strength score of 20 gives the character a unique powerful boost to melee damage.
Strength is the main attribute for heavy melee hitters that want to deal the highest damage in the game, being able to double-wield large weapons or hold massive 2-handed ones.
A character heavily focused on Strength wants to end a fight as quickly as possible with a small amount of devastating hits, stunning and knocking down its opponents, especially as it often lacks the physical and mental resources to sustain lengthy battles.