The off-hand is the non-dominant hand, which is always the left hand in Neverwinter Nights. (For simplicity of animations, all characters are assumed to be right-handed.) The off-hand can carry a torch, shield, or a secondary weapon for dual-wielding.
When dual-wielding, the off-hand weapon gets only half (rounded down) of a positive strength modifier as bonus damage. If the strength modifier is negative, the full penalty (not half) will apply. The off-hand weapon also gets fewer attacks in most (but not all) cases, which is one reason for not using one's best weapon in the off-hand.