A card can't be destroyed and damage can't be dealt to it. However, the card may still be exiled or if it's a creature, "killed" via minus toughness effects like Infest.
Example: Darksteel Colossus is in play and blocks a 20/20 Knight of the Reliquary. Darksteel Colossus doesn't die because it is indestructible but it still had 20 damage dealt to it. If the Darksteel Colossus had protection from white or something, the damage is prevented, so it is NOT the same as protection.
700.4. If a permanent is indestructible, rules and effects can't destroy it. (See rule 701.6, "Destroy.") Such permanents are not destroyed by lethal damage, and they ignore the lethal-damage state-based action (see rule 704.5g). Rules or effects may cause an indestructible permanent to be sacrificed, put into a graveyard, or exiled.
Basically:
If it would be destroyed by lethal damage, it isn't
If it would be destroyed through the means of Doom Blade, Wrath of God, or Naturalize (depending on the indestructible permanent), it isn't.
If it's a creature and its toughness is reduced to 0 through the means of -X/-X (Mutilate or Disfigure, for example), it still dies because this isn't destruction
Example:
Darksteel Colossus is in play and blocks a 20/20 Knight of the Reliquary. Darksteel Colossus doesn't die because it is indestructible but it still had 20 damage dealt to it. If the Darksteel Colossus had protection from white or something, the damage is prevented, so it is NOT the same as protection.
Basically: