This is an often life-saving shield, especially while being pounded on by multiple enemies, such as in arenas.
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. 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, enemies will have been destroyed or fairly weakened by teammates.
Patch 6.0.2 (14-October-2014): Pain Suppression no longer reduces the target’s threat by 5%.
Patch 5.2.0 (5-Mar-2013): Pain Suppression and Guardian Spirit can now always be cast while stunned.
Patch 4.0.6 (8-Feb-2011): Pain Suppression is no longer dispellable.