It's not really about dying from smallpox, or the black plague, or anything.
Many have associated the poem with the Great Plague of London in 1665, or with earlier outbreaks of the Black Death in England. Interpreters of the rhyme before World War II make no mention of this; by 1951, however, it seems to have become well established as an explanation for the form of the rhyme that had become standard in the United Kingdom. Peter and Iona Opie remark: "The invariable sneezing and falling down in modern English versions have given would-be origin finders the opportunity to say that the rhyme dates back to the Great Plague. A rosy rash, they allege, was a symptom of the plague, posies of herbs were carried as protection and to ward off the smell of the disease. Sneezing or coughing was a final fatal symptom, and 'all fall down' was exactly what happened." The line Ashes, Ashes in alternative versions of the rhyme is claimed to refer variously to cremation of the bodies, the burning of victims' houses, or blackening of their skin, and the theory has been adapted to be applied to other versions of the rhyme. In its various forms, the interpretation has entered into popular culture and has been used elsewhere to make oblique reference to the plague. (For 'hidden meaning' in other nursery rhymes see Mary, Mary, Quite Contrary, Humpty Dumpty, Jack Be Nimble, Little Jack Horner, Cock Robin, and meanings of nursery rhymes.)
Many folklore scholars regard the theory as baseless for several reasons:
1.) The late appearance of the explanation;
2.) The symptoms described do not fit especially well with the Great Plague;
3.) The great variety of forms makes it unlikely that the modern form is the most ancient one, and the words on which the interpretation are based are not found in many of the earliest records of the rhyme (see above);
4.) European and 19th-century versions of the rhyme suggest that this "fall" was not a literal falling down, but a curtsy or other form of bending movement that was common in other dramatic singing games.