Animal magnetism can refer to three things:

Franz Mesmer's theory and its professional use in healing practices, and associated metaphorical uses of the term.
Any of several exhibitions of Animal magnetism presented as theatrical events by showmen over the years.
A play by Elizabeth Inchbald

Mesmer and the term Animal magnetism

Animal magnetism [1] is the English version a German term "Lebensmagnetismus", a concept evolved by the German doctor Franz Mesmer in the 18th century to refer to what he believed to be an invisible natural force possessed by all living things, including humans, animals, and vegetables, a force that could have physical effects, including healing. He tried unsuccessfully to achieve scientific recognition of his ideas. However, his treatments, referred to a "mesmerism", were to become the forerunner of hypnosis as a medical tool, a term given coined by the Scottish surgeon, James Braid, in response to an 1841 exhibition of "animal magnetism", by Charles Lafontaine, in Manchester[2].

The term is of course the source of the notion of someone being "mesmerised" and the colloquial reference to an individual's sexual attractiveness or charisma as his/her "(animal) magnetism".[3]

The term is also found as a reference to Magnetoreception, the animal sense which detects magnetic fields to perceive direction, altitude or location, or metaphorically and colloquially, an individual's sexual attractiveness or charisma.[4]

Animal magnetism as a performance event

Exhibitions of Animal magnetism by "mesmerists" were presented as theatrical events by showmen over the years, from the very inception, in much the same way as various hypnotists would travel and display their skills at hypnotism as public performances, even to this day. Often part of vaudeville and music hall programmes, as well as afterpieces to plays.