Can be used even when stunned, serving as a very helpful panic button when surprised by rogues or warriors in PvP. When healing others, this feature also allows the priest to provide a substantial amount of damage mitigation for their target while stunned, such as when opposing players are attempting to CC (crowd control) the priest.
Although a powerful tool, like many of the Discipline priest's abilities, Pain Suppression's strength lies in preventing damage. Timing and anticipation of incoming damage is therefore key to making the most of it. Pain Suppression is best used just before the target takes a large amount of damage; since it is not on the global cooldown, priests can pop this then focus on shielding and healing the target. When used in this way, priests can allow their targets to survive an otherwise overwhelming onslaught. Since it has only an 8-second duration, waiting until the right moment to cast it is critical.
Pain Suppression really shines in a PvP or Arena situation. No one likes to have their enemies healed, so healers are often "target #1" and focused on by many enemies at once, especially in arenas. A common strategy for an opposing group is to all simultaneously blow their most powerful cooldowns and spells on the enemy's healer. To avoid being instantly knocked out of the game, a priest can pop this spell in an attempt to survive the onslaught. If used with any combination of fear, shield, or grenade, and heals; it is possible to survive an otherwise hopeless situation. Hopefully, while the priest was the focus, his enemies will have been destroyed or fairly weakened by teammates.
Patch 7.0.3 (2016-07-19): Cooldown increased from 3 minutes to 4 minutes.
Patch 6.0.2 (2014-10-14): No longer reduces the target's threat by 5%.