Ring around the rosie(1),
A pocket full of posies(2),
Ashes, ashes(3) -
We all fall down(4).
1) The symptoms of the plague included a rosy red rash in the shape of a ring on the skin.
2) Pockets and pouches were filled with flowers, incense, and herbs to ward of the disease or to mask the smell of death.
3) Refers to the cremation of the bodies or the burning of victims' houses, or may approximate the sound of sneezing, another symptom of the plague.
4) May refer to dying, but alternatively to a curtsy.
The idea that this historical nursery rhyme dates back to either the Black Death (bubonic plague) in Europe in the 14th c. or the Great Plague of London in 1665 seems at first entirely plausible. But it is not true! The song wasn't being sung until the 1790s, and wasn't printed until 1881. It is a rhyme of indefinite origin and no specific meaning, and was "retrofitted" with a believable explanation.
Sources: Wikipedia, Snopes