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Ring-around-the-roses is, as mentioned in the OP, a nursery rhyme. It is also a common children's game, at least in the US. The exact words vary, as is true of all playground rhymes, but this is the version with which I'm most familiar.
The whole line is: Ring around the rosy, pocket full of posies, ashes, ashes we all fall down.. This was a song that children used to sing when the black plague was an epidemic. It describes the symtoms- often times the first signs of the black plague would be a ring around a red spot on the skin.