John, Michael Quinion always does a great job of sorting things out and is, from my experience, a source to be trusted.
World Wide Words by Michael Quinion
JUMBO: Many people, especially here in Britain, would immediately think of the famous African elephant of that name at London Zoo.
Jumbo arrived from Paris on 26 June 1865 and he remained in London for years, giving rides to thousands of children and becoming a great favourite with the public. When fully grown he was the largest elephant known at the time, standing 12 feet tall and weighing over six tons. However, the Zoo became worried that Jumbo was getting very cantankerous and difficult (bull elephants are notoriously hard to keep captive) and that he would become a danger to his keeper and to the public. The Zoo sold him to Barnum and Bailey’s Circus in 1882 (he was sadly to be killed by a train in Ontario three years later).
The sale aroused huge passion and indignation, including a protest from Queen Victoria. You can judge his popularity from a comment in Mark Twain’s Following the Equator about Barnum’s intending purchase of him: “Jamrach said it was no use to think about it; that Jumbo was as popular as the Prince of Wales and the Zoo wouldn’t dare to sell him; all England would be outraged at the idea; Jumbo was an English institution; he was part of the national glory; one might as well think of buying the Nelson monument”.
Jumbo the giant elephant certainly popularised the name as an epithet for something of large size and you can find many examples recorded from the 1880s onwards. His influence was greatest in North America, where Jumbo became a great attraction during his short residence (Thomas Alva Edison, always the publicity hound ready to jump on a popular bandwagon, named one of his new electric dynamos “Jumbo” in 1884). The word has been around ever since, especially in North America, as a neat way to describe anything large of its type, and led to compounds like jumboburger, jumbo-sized, and jumbo pack. Walt Disney clearly had him in mind when he named his cartoon elephant Dumbo. However, the introduction of the jumbo jet in the 1960s helped to move the word into international English and to popularise it more widely.
Jumbo the elephant, though, is often said not to be the origin of jumbo the word, because it has been found in an 1823 work about racing in reference to a big clumsy person. However, this appears just once, with no further examples turning up until after Jumbo had become famous. It is possible that the older word was not in fact the source (though we have to remember that slang terms were often very badly recorded at this period). It’s also suggested that Jumbo got his name from mumbo-jumbo, a word for a West African deity (inappropriate, as it happens, because Jumbo had been captured on the other side of the continent). Oddly, though neatly, mumbo-jumbo is also thought to be the origin of the earlier slang jumbo.
The most plausible suggestion is that given in W P Jolly’s book of 1976 about Jumbo. He says that his keeper at London Zoo gave him that name—soon after he arrived—from the Zulu jumba, a large packet or parcel (which he certainly was: even as a rather sick four-year-old, Jumbo was five feet high and weighed about half a ton).