Armor hit points reduce incoming damage, and shield regenerates. According to this reddit post, shield depletes before armor, and one reddit commentor describes this effect to be extremely useful:
Torbjorn armor put on Zarya effectively turns her large shield pool into an armor pool, because shields deplete before armor, but armor provides the reduction as long as it's in your health pool.
But is this actually the case? It doesn't make much sense for armor to cause damage reduction to shields, however, if it does, that's definitely an interesting synergy.