Magic

Magic (魔術) is a term used to refer to supernatural phenomena that cannot be explained or analyzed via any sort of scientific means and reasonings. In the Toaru Majutsu no Index universe, magic is a complex system of arts, disciplines, and traditions that are firmly grounded in laws and knowledge that are wholly unknown and beyond the grasp of human sciences, which sought to manipulate and distort certain aspects of reality.

Also called the occult, conflicts with the magic side, the secret underworld that deals with magic and the occult, are the primary and most recurring plot points of the series.

History
Magic by itself roots from the simple fact that 'those without talent' wanted to be able to do the same things as 'those with talent' - namely Esper and Gemstones.