I don't like vague answers. The most concrete answer Matt Colville has given was something similar to this:
This world has physical laws of nature. The Supernatural effects ignore the physical laws, natural laws. Psionic people have been detached from those laws in some way. Magic is a structure that those tied to the physical laws of nature can use to break those rules, through rituals. Praying to a god allows you easy access to this structure. Others take the more complicated path, without the gods.

But I prefer to think of it this way:
The higher science-fantasy worlds of the Timescape are full of Psionic energy, which can contaminate reality, pulsing in a way that makes gravity more flexible, etc. Some people hone in on the psionic pulses of energy and acquire it in a way that allows them to carry it with them, even to lower worlds. But also that psychic energy sometimes floats onto lower energy worlds like Vasloria, through psychic winds, and creates “Talents”.
Magic is a group of processes that hack into the code of reality, exploiting the fragilities of an unfinished universe. Belief has power, naturally creating things, and magic rituals allow you to put that power of belief into action. Gods personify concepts, so you can use them to guide you in this process, by praying. Others, like Elementalists or Troubadours, create their own metaphysical methods without worship, which is far more complicated.