More specifically, it's what is known as a state trigger. Usually triggered abilities look for an event to happen to trigger. State triggers look for a certain game state to be true. What makes state triggers special, though, is that they won't trigger again until the ability leaves the stack. This rule (603.8) is what prevents the infinite triggering that the comment on gatherer is talking about (Opal Avenger will only be a Creature and not an Enchantment, and the intervening if prevents it from triggering once it has resolved the first time).
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Is the ability a triggered ability or a "state-based" ability ?
On modo it is a triggered ability, but a comment on Gatherer says it is a "state-based" ability.