"Where Magic is concerned, there's always an initial decision, an initial willingness to let it into your life. If that is not there, neither is Magic"- Mister E 
Magic, often referred as The Art, is a dangerous, invisible and all-powerful force that many humans and creatures come into in contact with. People who uses magic are often called magicians, magus or wizards (witches for female).
Magicians use the Art to wield mystical and metaphysical forces and study occultism, the inner truth existing below the material surface: the truth is hidden in plain sight. One of the most interesting aspects of the Art is it's interaction with science with is at odds due to the irrational and supernatural nature of the former. Science is based on the natural, reproducible and logical, neither of which magic is.
Unlike science who is dependant in the physical nature of the universe, magic is metaphysical, who is driven by other metaphysical objects such as vigor, courage, or evil. But like science it also has logic, as logic is the universal truth and answer, thus magic can be obtained through many sources such as energy and demonic powers.
Magicians in the Hellblazer mythos differs greatly from the ones in traditional comics. It is because magicians in the series leans towards realism and historical recordings rather than the fantasy driven magic. This is a reason why many Vertigo stories calls it Magick to diffferentiate them from "magic" which means fictional fantasy powers. Because of its realism, magicians in the Hellblazer series are almost depicted as nigh-omnipotent and spontanious like sympathetic magic and synchronicity wave travelling, rather than the glamorous shoot-fire-from-your-wand magic from from traditional fantasy fiction (though demons and powerful magic users have been seen to do this type of magic e.g Alba has shown telekinetic ability and the wizard Rinzen was shown throwing balefire). Also, unlike some fantasy magician that is sometimes limited by "mana" or other forms of energy, magic in the series is all-powerful and unlimited, but it can be increased and empowered by factors such as sacrifices, arcane knowledge, and making dealing with celestialbeings. It can however be limited by the magician's magical knowledge.
The Occult History
When the universe was first created by God there was a glowing city named Heaven where God's servants, the angels, lived until one rebelled against the celestial hosts. The rebel angels lost the war and were expelled into the Chaosplasm which mutated to a fiery realm named Hell; the angelic beings mutated into horrific monsters known as demons.