A jacuzzi is named after a family, not an idea. The Jacuzzis came from Friuli, in northern Italy, and the word for the bubbling tub is their surname.
Etymonline dates the word to 1961, as a U.S. proprietary name for a whirlpool bath, taken from Jacuzzi Brothers. It adds that the brothers had earlier built jet pumps for motorboats and that the family emigrated from Friuli. Dictionary.com is less sure, dating first recorded use to 1965 to 1970 with a note that one source says 1961. Wikipedia places the family's home town as Casarsa della Delizia.
The seven siblings had all emigrated to the United States by 1910 and founded a company in Berkeley, California, in 1915. They started with aircraft propellers, then moved into hydraulic pumps for irrigation.
The bath came out of a family medical need. Candido Jacuzzi built a hydrotherapy pump for his son Ken, who had rheumatoid arthritis. Sources agree it was a portable pump that turned an ordinary bathtub into a spa, but they differ on dates. Wikipedia says Candido developed it in 1948, patented it in 1952 and marketed it around 1955 or 1956. The company's own history dates the J-300 pump to 1956.
The self-contained tub came later. The company's history credits Roy Jacuzzi with the Roman, a whirlpool bath with built-in jets, in 1968. It moved the product from medical treatment toward home luxury. The family sold the company to Kidde in 1979 for about $70 million, and it has changed hands several times since.
Because the company dominated the market, the name came to mean any hot tub in American English. That is a classic trademark problem. The Associated Press Stylebook still treats Jacuzzi as a trademark. Etymonline's Taser entry lists other brand names that have drifted the same way, including Photoshop, Polaroid and Dumpster.
I could not find a source on what the surname itself means, so this page does not guess. The reliable point is the direction of travel: from a family name, to a company, to a bath, to a generic word.