Actually, Vigilant is a bit more complicated than Lars states because the rules for Vigilant say you may stand Vigilant characters after winning the challenge. You actually could choose not to stand a Vigilant character.
But Vigilant is considered a passive effect, not a triggered effect. The reason why is tricky, so bear with me. It works out like this:
1. You win a challenge.
2. According to the rules for Vigilant, you now must resolve the keyword.
3. Resolving the keyword means you make a choice, for each Vigilant character, to either stand or not stand them (guess which choice people usually make...)
The thing that makes Vigilant a passive effect is #2. You must resolve Vigilant when you win the challenge whether you want to or not. Now, an acceptable resolution of Vigilant is to choose not to stand the character, but when you make that choice, you have still resolved the Vigilant effect. If it were a true triggered effect, you could refuse to resolve it completely. It's a bit confusing because completely refusing to resolve Vigilant and choosing not to stand the character during resolution of the keyword amounts to the same thing (a knelt character). But conceptually, they are very different things.
It's worth noting that Vengeful and Stealth both have similar elements of "passive choice."
So perhaps it would have been more accurate to say that the defining characteristic of a "triggered effect" is player choice concerning whether or not the effect initiates in the first place. Vigilant, Vengeful and Stealth (which are all passive) give the player a choice in how the effect resolves, but there is no choice as to whether or not the effects initiate.