Indestructible prevents a permanent from being destroyed by effects that say "destroy" and prevents lethal damage from destroying a creature. It does not protect against exile, sacrifice, having 0 toughness, or several other forms of removal.
Boros Charm can give your permanents indestructible for a turn, while Selfless Spirit can sacrifice itself to protect your creature team. Darksteel Citadel demonstrates that the ability isn't limited to creatures.