The rash that the boubonic plague showed was a ring on the skin. Pockets were filled with rose petals and herbs because they believed the disease was carried by bad odors (rats were the culprit, specifically fleas on the rats). Ashes, Ashes is the reminder of cremation to help control the plague.
Ring around the rosy
A pocketful of posies
"Ashes, Ashes"
We all fall down
Ring-a-Ring o'Rosies
A Pocket full of Posies
"A-tishoo! A-tishoo!"
We all fall Down!