The strength modifier is added to melee attack rolls (unless weapon finesse allows the dexterity modifier to be used instead) and to damage rolls. Furthermore, the strength modifier is added to the discipline skill.
There are some special rules concerning the strength modifier and damage rolls. For ranged damage, less than the full strength modifier might be used depending on a weapon's mighty property. For melee damage from a two-handed weapon, 1.5 times the strength modifier is used. For melee damage from an off-hand weapon, half the strength modifier is used. Fractions are rounded down. A double-sided weapon is treated as two one-handed weapons for the purpose of determining how much of the strength modifier is added to damage (i.e. the full modifier for the main-hand side and half that for the off-hand).