In PvP, opponents will often stop attacking you when you are Dispersed, but may also CC you to prevent you from fleeing.
In Raiding, Dispersion is a very powerful cooldown, as it is one of the very few abilities that allows a single player to "soak" lethal boss abilities that often require two or more players.
Dispersion can be used while mounted. This can make it particularly useful for escaping ambushes when mounted, as priests can use Dispersion to survive attacks and swiftly ride away, outstripping their unmounted attackers.
Patches and hotfixes
Patch 8.1.0(2018-12-11): Dispersion now reduces damage taken by 75% (up from 60%), and additionally provides 50% increased movement speed for the duration. Now available at level 28 (was level 48).
Patch 7.0.3(2016-07-19): Damage reduction effect decreased to 60% (down from 90%). Additionally, Dispersion now prevents [Voidform] from draining Insanity while active. Now available at level 58 (was level 60).
Patch 6.0.2(2014-10-14): Dispersion no longer restores mana (was 6% every sec).
Patch 5.2.0(2013-03-05): Now belongs to the Shadow spell school.
Patch 5.0.4(2012-08-28): No longer a talent. Now a baseline ability for Shadow.
Patch 3.2.0(2009-08-04): Cooldown reduced to 2 minutes (down from 3 minutes).
Patch 3.1.0(2009-04-14): Now clears all snare and movement impairing effects and makes you immune to them while dispersed.