Blue Mage has always been about learning enemy abilities and using them for your own benefit. There was never really any lore beyond that in any of the games except XI, which was actually kind of dark.

In that title specifically, your character is essentially kidnapped and your soul is shattered via Aht Urghan alchemy to allow for you to absorb the essence of monsters. (I may be wrong about the kidnapping part, it's been very long since I did that). The soul-shattering aspect was the in-game explanation of the "how" behind the blue magic abilities and could lead to people unable to contain said power turning into Soulflayers. This didn't actually happen to players, it was just an explanation for where the enemy type came from.

in XIV, it's more about <insert lore here when we get it>. ¯\_(ツ)_/¯