What Even is Magic?

If you happen to be a materialist, it can be easy to unlearn what magic is supposed to do. Some people say that magic, as opposed to the natural world, is somehow not scientifically observable. This is not quite right. If you have a ritual that can be used to summon the demon Valtherastices, then by induction we can say, very scientifically, that we did some tests and found that the ritual, in fact, summons Valtherastices. Spells in fictional settings, and for the most part in the imaginings to real-life practicioners, do actually have observable effects-- why else would people perform them?
Even when the effect is low, like a spell that has only a 2% chance to summon Valtherastices, or when it is distant, like he may only appear years later, the spell can still be empirically verified once your wizards start introducing double-blind experiments and large sample sizes. "Hmm, looks like .03 of the group that performed the ritual summoned Valtherastices after two decades, and only 0.01 of the control group did. That's a p-score we can feel confident in."
So magic is not about an uncertain effect. It is not, in that way, mysterious. Having a system, such that might be studied in a wizard's college or an alchemist's lab, does not make magic unmagical or a mere branch of science. What is different is the connection. The natural world only allows an effect if the cause can somehow push the matter of the world to make that it happen. A wire carries an electric current because of the direct interaction of elections along every step of the line. Magic does not work like this. Magic ties a cause to an effect without necessarily manipulating matter in this same lawful way. Magic does not work through nature, it is above nature. Hence, supernatural.
Sure a ritual may require you to make a physical connection or satisfy material conditions, but this merely activates the magic. It is simply a correspondence, like pre-established harmony. When the connection between a particular cause and effect are unknown in physics, physicists start trying to figure out what that connection could be. In this way, they predict things like the Higgs-Boson before actually discovering it. In magic you cannot do this, because there is nothing to predict. It is simply a black box that checks if a condition is met, then spits out an answer.

A diagram of a human's rifle, which uses combustion and other chemical reactions, can explain each step, in increasingly fine detail. A diagram of an orc's rifle, which uses psychic power, can only explain on the level of "IF there is metal in the clip, THEN magic makes bullets shoot out of the barrel."