A magic system is a set of rules that regulate the magical effects that can be produced in a fictional setting. It is an element that sets fantasy fiction apart from other genres. For a story to be considered fantasy, it needs to contain some sort of magic system.
A magic system refers to things that occur or exist in your story that do not or cannot exist in the real world. Elements of sorcery, witchcraft, enchantments; fantastical creatures, the supernatural and advanced abilities or powers.
Consider the following:
Define its use – How does a user summon magic? How does that magic manifest? What fuels the magic? The consequence of using magic, if any?
Identify users – What do you call magic users? Is magic inherited, gifted, obtained or learned? Are there multiple types of magic users – and if so, what differentiates them?
Limitations – Is magic a limited resource? Can it be stolen or suppressed? Does it affect the user? Does the magic make the user invincible? How do you defeat a magic user?
Dangers of magic – Can magic be used to cause harm to others? Can it be used incorrectly or immorally?
Origins of magic – How was magic created? Where does it source its power? Are there different types of magic? History of magic – any important historical events where the world was affected by the use of magic?
Culture of magic – Is magic a secret in your story? Are there any magical societies or a hierarchy of magic users? Can magic users be identified by their appearance, clothing? Do users of magic have their own language, religion, festivals, etc?