Well what I've ended up with right now is :
- We're talking about a journey that probably went like this :
Besaid - Kilika - Thunder plains - Macalania Temple - Al Bhed Home - Bevelle - Calm Lands - Zanarkand. (They're referring to the lines respectively, except for the 2 last ones).
So ALL this journey will give us immunity and stamina like a diety.
If it weren't about TP and Home the answer would have been the Aeons.
Oh wait...it's not the sphere grid is it?
(then perhaps the first line refers to the origin of the sphere grid rather than Besaid - origin of yuna's pilgrimage)