I realize this might be a silly question, but in the context of the Elder Scrolls universe how does the gameplay mechanic of perks and perk trees translate to in-universe?

Perks are just another gameplay representation of how skills work. As you hone your skills and practice, you learn different tricks like how to harvest more ingredients from a plant, or use lightning spells to disintegrate your enemies. Or, you develop passive abilities like a resistance to magicka or more efficient item storage (Deep Pockets).

You might enjoy reading the in-game skill books, if you don't already. Twin Secrets describes how the Extra Effect perk works, for instance.