Basically it just describes what happened to the bodies of those who contracted "the plague" a rosy red rash in the shape of a ring would cover the body, pockets full of posies -(they believed that the smell was the cause of the plague) so the sweet smell would protect you, ashes, ashes--the bodies were cremated .
This is because people often associated it with the bubonic plague that swept through Europe. The line in the song "Ring around the Rosie" was referred to as the red X mark that was drawn on the doors of people as a warning that someone had died or was going to die from the plague. Check out bussongs.com for more details.
Ring around the rosie= circular sores with the blisters in them!! pocket full of posies= they would put flowers in their pockets to help mask the bad smell from the sores!! Ashes ashes we all fall down= they die and the bodies would be burned!!! I'm not saying its a bad song but it does have a very dark, negative story behind it!!