the pilgrimage of a summoner is the journey that a summoner makes.
they go to every temple to gain aeons then they get to zanarkand. when theyre at zanarkand they must sacrifice one of thier guardians to become the final aeon then using that aeon they defeat sin and then theyre final aeon becomes the new sin after theyre pilgrimag comes the calm
<in yuna's case however she refused to sacrifice one of her guardians and that is why sin died (theyre was no final aeon to become sin)>