Totem Armor is a keyword ability that appears on many auras from Rise of the Eldrazi. It is a static ability that generates a replacement effect. This replacement effect is applied when the enchanted creature would be destroyed by an effect or a state-based action. Instead of having the creature go to the graveyard, the totem armor is destroyed and all damage that was on the creature is removed.
If a creature has more than one totem armor aura on it when it would be destroyed, then the controller of that creature would choose which of the two auras is destroyed instead of the creature being destroyed. This is because when two or more replacement effect are both trying to affect the same event, the controller of the affected permanent chooses which to apply first. Then if the other can still be applied, it is. In this instance, the second replacement effect cannot be applied as the creature is no longer being destroyed.