Your cousin or lab partner or bus buddy explained that victims of the plague would get red, rosy rashes around their eyes. They would lean in real close and explain that "pocket full of posies" refers to the fact that people carried flowers in their pockets to cover the smell of rotting flesh. Then their voice drop to a whisper as they told you about the "ashes, ashes" of the burning bodies after they had succumbed to the disease. And "all fall down?" Well, that's just too easy. It's death death death.
But your cousin or lab partner or bus buddy was wrong.
According to folklorists, it's just not likely.
First of all, this theory wasn't even popularized until the 1950s. But the nursery rhyme was first printed in 1881. It seems like this theory would have been discussed sooner if it was based on horrifying world history.
Second, there are several versions/verses of the rhyme and most don't fit the black plague theory at all. Here are a few for reference:
Ring a ring a rosie,
A bottle full of posie,
All the girls in our town,
Ring for little Josie.
Round the ring of roses,
Pots full of posies,
The one stoops the last
Shall tell whom she loves the best.
Ring-a-ring o’ roses,
A pocket full of posies,
One for Jack, and one for Jim,
And one for little Moses.
A-tischa! A-tischa! A-tischa!
Ring, a ring o’ roses,
A pocket full o’ posies,
Up-stairs and down-stairs,
In my lady’s chamber —
Husher! Husher! Cuckoo!
Here's a version that doesn't mention a ring of rosies at all.
Cows in the meadows
We all jump up.
Also, the "rashy eyes" or violent sneezes (another possible explanation of "ashes, ashes") don't really match with real symptoms of the plague.
According to the Mayo Clinic, symptoms of bubonic plague include "swollen lymph nodes, which can be as large as chicken eggs, in the groin, armpit, or neck. They may be tender and warm. Others include fever, chills, headache, fatigue, and muscle aches."
They also say to get medical attention if you think you have the bubonic plague.
Finally, "all fall down" is probably a reference to some kind of curtsey rather than death. Apparently this was all the rage among singing games of the day.
So what's it really about? Most likely answer: nothing. It's just silly words for children to sing. Folklorist Phillip Hisock says:
"The rings referred to in the rhymes are literally the rings formed by the playing children. “Ashes, ashes” probably comes from something like “Husha, husha” (another common variant) which refers to stopping the ring and falling silent. And the falling down refers to the jumble of bodies in that ring when they let go of each other and throw themselves into the circle."
And so? There you go. Everything is a lie and poetry means nothing.