The energy that fuels magic and other "supernatural" events is the same energy that makes up the souls of living beings. Anima. Anima is formed within a soul when the soul creates new memories, grows, absorbs information--in general, through the process of creation. When a living thing dies, its spark (the portion that creates anima) passes into the Shadows (for intelligent beings) or back into the Prime plane (for plants and lower animals). That energy is pumped up into the astral by the Great Mechanism and passed among the gods and used to maintain the universe itself.
Living spell-casters accumulate anima in knots in their souls. These knots come in varying strengths--two lower level "slots" do not equal one higher slot. These knots are used to fuel patterned resonances with the ambient anima--these patterned resonances are spells. Some spells (cantrips) can be cast solely with the caster's mental energy and do not use up these knots. Without special training, these slots reform over time but require a night's rest to be usable again. There are rumors of some who can force energy into their knots faster, but those are not widespread.
The number of spell-slots available to a caster depend on their level of soul-growth. For many (if not most) people, the ability to cast a single (or at most two) of the lowest-powered spells is the maximum they will ever attain. Some grow quickly, some more slowly. Those who focus on spell-casting tend to grow faster than those who split their efforts with martial pursuits.
While all spell-casters gain power from the ambient anima, the source of the spells (that is, the patterns through which they manipulate reality) differs. Those differences are described in The Varieties of Magic.
Since all magic is mediated through souls, permanent magical items that can actively manipulate anima (cast spells or spell-like effects without needing to be recharged) are vanishingly rare. In fact, some theories suggest that imbuing an item with enough anima to persist and gather anima by itself would by necessity involve the creation of a soul (and thus would make the item intelligent to one degree or another). Temporary magical items such as scrolls, potions, or Spellstones (stones that can be charged to unleash magical energies) exist but the creation of these requires an intelligent being to contribute anima and, once used, are rendered inert or destroyed.