The word galvanize honors a theory that turned out to be wrong.
Luigi Galvani was a physician and anatomy professor in Bologna, born in 1737. Over many years, from about 1780, he ran electricity through the legs of dead frogs and watched the muscles twitch. In 1791 he published his main work, a Latin commentary on the effect of electricity on muscular motion. He argued that animal tissue produced its own electricity.
The physicist Alessandro Volta repeated the experiments. Volta came to doubt the theory and argued that the twitching depended on the metal conductor linking nerve and muscle. Merriam-Webster notes that Galvani's idea of a special animal electricity was later disproven. The two men disagreed respectfully, and Galvani's nephew, Giovanni Aldini, took up the public defense.
Yet the name stuck to the phenomenon. French produced galvanisme, electricity produced by chemical action, and galvaniser, to apply it. Sources differ on who coined the terms. Wikipedia credits Volta with "Galvanism." Merriam-Webster says Alexander von Humboldt apparently coined the French words, modeled on magnétisme and magnétiser.
English followed quickly. Etymonline dates galvanism to 1797 and galvanize to 1801, meaning "to stimulate by galvanic electricity." Merriam-Webster gives 1802. Galvani himself died in December 1798, in poverty after refusing a loyalty oath to the new Cisalpine Republic.
Two later senses came from the same root. In 1839 galvanize gained its industrial meaning: coating iron with metal by galvanic electricity. Etymonline says this first meant plating with tin and now usually means zinc. It records the sense first in the phrase galvanized iron.
The figurative sense came from the twitching frog itself. Galvanic was used figuratively by 1807, and Etymonline dates galvanize in the sense "excite, stimulate, as if by electricity" to 1853. Merriam-Webster says the figurative sense, spurring people to action as if by a shock, is now the main one.
The experiments also reached fiction. In her 1831 introduction to Frankenstein, Mary Shelley recalled talk of whether a corpse could be brought back to life. "Galvanism had given token of such things," she wrote.