Your strength determines your ability to use weapons and armor. You begin the game with 12 strength and gain an additional point every time you drink a potion of strength. Some enemies like centipedes and dart turrets can temporarily lower your strength.
Strength modifies the effective enchantment level of any weapon or armor that is equipped. Each point of strength above the item's requirement allows you to use the item as if its enchantment level were 0.25 higher. Conversely, each point of strength below the requirement causes you to use the item as if its enchantment level were 2.5 lower.
The overall effect is that excessive strength causes your weapons and armor to be slightly more effective and insufficient strength causes your weapons and armor to be much less effective.
Applying a scroll of enchantment to a weapon or armor lowers its strength requirement by a point as well as increasing its enchantment level.