What is Magic? Well one way it's framed is being the opposite of Science. A wizard casting a levitation spell or a 20 meter long armored reptile flying about shooting fire from it's mouth without burning it's jaws off or a animated clay statue is something which operates outside the laws of physics as we know them. But here's the thing, in another world where things are different magic could be just another set of laws which can be observed, experimented on and repeatable results and predictions can be made to expand one's understanding of the nature of Magic. In that case, the study of Magic eventually becomes just another school of scientific thought. Probabily one with a lot of rituals and fancy ornaments, but Scientific none-the-less. Many fantasy worlds have made very good use of this outlook of things one way or another, but there are those which want to avoid it.
One of the most popular ways to get around this is the idea of Belief Function. If you drop an object on Earth in a vacuum it will accelerate at 9.8 meters per second per second towards it's center until it hits ground. You can rant and rave about how Issac Newton was an idiot and his ideas are hogwash all you want, believe that this is not the case in the depths of your soul and plead and pray for this not to be the case with all your heart, the rock will still fall in accordance to the laws of gravity. The Universe does not care what you believe, it simply is. In a world with Belief Function, things are different. Reality is shaped to some degree or another by what people believe, especially in aggregate. In those worlds enough belief can disrupt that constant, or create someone who intervenes to do so.
A related concept with a lot of crossover to Belief Function is Emotion Function, in which magic is dependent on the Emotional State of the person wielding it and emotions can have an impact on reality.
Examples of Belief Function
- Discworld: Belief is a powerful force. The Gods exist due to belief and wither away once belief in them fails.
- White Wolf's Technocracy is built around Belief Function
- Warhammer (Both Fantasy and 40k)