History of Suppression

Suppression is a Void debuff. The D2 Wiki says it takes the target out of any active abilities, stops it from activating abilities or movement modes, and stops combatants firing their weapons; it stuns Overload Champions. DualShockers adds that it can shut down a Super in the Crucible and disable Hive Guardians' abilities.

Sources

DualShockers (an older article, so check for later additions) lists three ways to apply it: the Shadowshot Super, the Suppressor Grenade, and weapons, namely Collective Obligation (which leeches Void debuffs such as suppression and re-applies them) and the Tractor Cannon.