Anton Franz Mesmer was a German physician in the 18th Century experimenting with magnets to cure maladies. He began by using magnets and soon discovered that he did not even need them. He referred to his approach to curing as Animal Magnetism. Nobody at the time understood what was happening. In the 19th Century one James Braid studied what Mesmer did and proposed to call it hypnosis.
Mesmerised is a word derived from his name to describe a person who is completely captivated.