Paladin's source of power in game is all from within. It starts out as mere swordsmanship, augmented by aether, and it stays that way mostly. There aren't a lot of in game explanations nor suppositions about it. The willpower from a sense of nobility and duty becomes apparent in the 50~60 questline for it, but that was especially in relation to soul crystals, more than just raw power, as the PLD mentor Roegadyn did battle with you in that quest without a Soul of the Paladin.

So basically, the knowledge on how to manipulate aether comes from your Soul Crystal, and increasing your strength through battle experience allows you to unlock more abilities. This is the default for every job.