Its main purpose is to act as a type of damage prevention system similar to Terran fire suppression. By using phase shift technology, the dampener shunts explosions and energy discharges into a different dimension. Through the uses of multiple backups, Protoss buildings can take a large amount of damage without burning itself down as long as there are enough parts in normal space to function.
It is not limited to structures as some high level vessels use them to prevent destruction from internal threats (Stargate - SG-1: Explosion suppression system). In some cases, a Phase dampener is the only thing keeping a starship from being torn apart while under enemy attack.