Strength is a measure not just of your raw muscle mass, but also how well you can use that strength. Good Strength adds to the damage you do in combat, and some weapons need a high Strength to use effectively. Conversely, low strength reduces the damage you do. A Halfling warrior may be extremely quick and accurate, but he will do fairly poor damage when compared to a Dwarf! Strength also governs how much weight you can carry without being encumbered. Strength is a necessary stat for any fighting class, but is useful for magic-using classes as well, because no-one has an unlimited supply of magic! It is used when bashing down doors and in some instances for moving heavy objects.
Strength increases your maximum damage roll according to the following chart:
STR Damage STR Damage 20 -3 90 +4 30 -2 100 +5 40 -1 110 +6 50 +0 120 +7 60 +1 130 +8 70 +2 140 +9 80 +3 150 +10