Aegis Angel ‘protects’ another permanent in play by making it indestructible for as long as the Angel remains in play. This ability is an enters the battlefield (ETB) triggered ability. Because it is a triggered ability is uses the stack and therefore can be responded to. Once a player chooses a target for this ability, others can respond by destroying it before it becomes indestructible.

One other thing to note is that this ability does target, so permanents that have shroud will not be able to receive the Angel’s protection.