From “Origin of the Arcane Traditions” - by Kefarian Goldflame of Thuzaradin, Ninth Finger of the Hand.
… In essence, magic is the process of imposing and bending reality to a desired outcome through imagination.
To understand the process in simple terms, imagine yourself in a lucid dream. Within a lucid dream, you are keenly aware that the reality you inhabit will bend to your desire with a mere thought. In effect, magic applies this state of being to the waking world.
It is commonly understood that there are limits to what you can accomplish within a dream, such as reading a book. However, if one is lucid and imaginative enough, they can determine the words in the book and know what they are without reading them. In effect, by shifting your mind to no longer perceive the words but instead recall what they are, you alter the page to become that which you know it is, as opposed to what it might have been originally. In simple terms, if you happen upon a tome of alchemy in a dream, you can, through lucid control, alter the tome into a book of arcane basics. In doing so, you will know what it contains, and rather than reading the title, you will know the title from prior memory of it.
Magic works on the same principle. As you channel, you also alter the very perception of the building blocks that make up the world. You conjure fire without friction, you summon water without a source of liquid, and you alter rock and stone into shapes they always had, as determined by you. The world bends to your whim as if you were in a lucid dream.
This is, of course, a gross oversimplification of the process to help you understand the complex mindset required to perform magic. It first and foremost requires a great deal of imagination and creativity, not to mention the ability to detach oneself from the tethers of what is and is not true on a fundamental level. Thus, to perform magic is to deny everything that you know is true and insert your own truth in its place.
It should go without saying that it requires a special kind of mindset to perform magic. However, that is not the only way to perform it. Long ago, clever magi discovered they could write down their thoughts into less complex guides, spelling out the method in simple terms. These spells simplify the thought patterns in ways that allow even the most mediocre of magi to grasp and navigate the shaping of reality.
However, as no two individuals share the exact same thought pattern, this development has resulted in a bloated number of spell variants. On its own, I know thirty different firebolt spells. Each of them varies slightly, as do their methods. Some create smaller flames, some extend the range, some change the color and composition, and some even split the bolt into a multitude of smaller bolts. However, what they all have in common is the tangible bolt of fire the spell creates.
For all its complexities, a process designed to produce a firebolt will always create a bolt of fire. To put it in simpler terms, if three individuals invented the wheel, their methods would differ. However, the result would always be something similar to, or definable as, a wheel. …
(I decided to add some thoughts on how arcane magic works in-universe, but framed as a theory to give room for other interpretations.)