Magic (魔法 mahō) in the Nanoha universe refers to the shaping of magical energy (mana) into specific forms (spells) to achieve certain effects. As such, it is closer to science and technology than to mysticism.
All magic is powered by an energy called "mana", whose properties differ from person to person (e.g. most people have unique "magic colors", which determine their mana's default tint when they release it). Mages naturally acquire mana through their Linker Cores, a specialized organ that continuously collects mana that is dispersed in the atmosphere and stores it inside their body. Such replenishment is normally slow, but mages can replenish mana much faster by converting nutrients into it. To remain healthy, they require a balanced diet of sugars, carbohydrates, and proteins, as well as a variety of vitamins and minerals, therefore mages undergoing intense training during their early growth period usually eat a lot more than an ordinary person. In addition to regular mana replenishment, it can also be conserved in form of Cards or cartridges for later use, especially for combat.
The terms "mage" and "knight" refer to individuals who undergo training in and master magic. Before mana can be used for a particular purpose, the mage uses their Linker Core to shapes it into an appropriate form in a process known as "linking". Since efficient linking requires complex energy calculations, predefined magical "programs" known as "spells" are created to simplify the invocation of common magical effects. These programs are computed within the caster's brain, assisted by their Device (which can also serve as a storage medium for spells). The visual manifestation of these calculations is a magic circle, and when they are complete, a trigger is usually required to release the magical energy. Once linked, the bonds of magic keep the energy together, unless dispelled or forcibly broken. An Anti Magilink Field (AMF) prevents the magical energy from being linked and such bonds, from forming, while EC Dividers can even break existing magical bonds.
Apart from the regular magical linking, some mages display the Mana Conversion Affinity, i.e. the ability to spontaneously convert their generated mana into another form of energy (electricity, heat), bypassing the calculations that mages without MCA require to achieve the same effects, while others learn to channel atmospheric mana directly into certain spells of the Breaker sub-type, bypassing their Linker Core and its capacity limits completely.