Strength measures the muscle and physical power of your character.
Some of the things which a character's Strength score affects are:
Attack Bonus and Damage with Melee Weapons- Strength makes it easier to hit with melee weapons, and makes you do more damage when you do hit. Additionally, you can apply your Strength bonus to damage rolls on thrown weapons and bows with the Mighty property.
Carrying Capacity- Characters with higher Strength scores can carry more weight before becoming encumbered.
This ability is especially important for Fighters, Barbarians, Paladins, Rangers, Monks and Swashbucklers because it helps them prevail in combat.