A check invokes a trait if it has or is against a card that has that trait.
Why would you want someone to have a hand size of 1? To keep them from dying. The bigger your hand size, the more cards you potentially have to draw when you reset your hand. If you can't draw a card, your character dies. A hand size of 1 limits your risk of death.
So Invoke is:
Traits transfer to the check from the card you encounter, and cards used on the check, as well as cards used to aid the check.
The Fate's Shepherd role card says:
"When a character at your location resets his hand, you may bury a card to reduce his hand size to 1 until the end of the turn. (#if the card you would bury has the Divine trait, you may discard it instead.)"
Why do i want my fellow adventurer(s) to only have one card in their hand until they reset their hand next round?