1. Originally, a system of therapeutics propounded by Mesmer.
2. A precursor of hypnotism, believed by Mesmer to involve animal magnetism.
3. By extension, the power to fascinate in a way that is almost hypnotic.

This term is named for the physician Franz (originally Friedrich) Anton Mesmer (1734-1815), who advocated his theory of animal magnetism or mesmerism. Mesmer stroked his patients first with magnets and later with his hands, believing he possessed animal magnetism. Mesmer's system of therapeutics was a forerunner of modern hypnotism.

An example from literature: "At first, when as a young man he began to dip into the secrets of mesmerism, his mind seemed to be wandering in a strange land where all was chaos and darkness, save that here and there some great unexplainable and disconnected fact loomed out in front of him." Arthur Conan Doyle, The Captain of the Polestar and other Tales, 1894, p. 84.