Sorcery (魔術 Majutsu) is the art used by all conjurers (魔術師 majutsushi) and mediums. Originally founded in ancient times as a way to combat creatures outside of the reason, it was the foundation for Magic Formula and its foundations. It costs magic element to use, and can be used only by people with inborn ability to control magic element.
The ability to use sorcery is inherited in a manner similar to genes, although how the sorcery can be accessed tends to vary. Conjurers are typically able to cast spells by incantations or motions, while Mediums require talismans, charms and the like. Usually conjurers can use nature elements for combat, like water, fire, earth, air, lightning, but some of them are able to manipulate gravity, use healing and defensive sorcery, and sorcery that boosts abilities.
Lycanthropes is a race created from sorcery, which makes existence of these creatures being outside of reason.
During the Great Dark War, Nine of the Ten Sages tried to teach people the art of sorcery to fight the Black Beast, but there were not many people able to learn it, so because of this, the Magic Formula was invented, which is a fusion of sorcery and science.
In the world of BlazBlue sorcery is barely mentioned, since that world has magic. In the world of XBlaze, there is no magic, so only sorcery is used there.