Casting Touch of Weakness applies a 10 minute buff to the Priest. When an enemy target successfully hits the Priest in melee, the target is hit for a small amount of Shadow damage (which can be modified by Shadow/general spell +damage) and a 120-second (2 minutes) duration debuff is applied to the target that reduces melee damage. This debuff does not stack.
Touch of Weakness can be very useful for a Priest who has invested heavily in the Shadow talent tree. Although the amount of damage that is reduced at high levels is fairly insignificant, the true power of Touch of Weakness is the Shadow damage component. Since Shadow damage is dealt to the target, Touch of Weakness will apply a charge of Shadow Weaving to the target (if the Priest has fully invested in the Shadow Weaving talent), and it also has a chance to proc Blackout, making it a useful tool against Rogues, Warriors, Enhancement Shamans, etc.