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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.
It's totally not obvious to a modern native speaker, even though the line is well-known from an old rhyme: Ring a Ring o' Roses. It has been claimed that it was originally a song about the Great Plague of London but this is dubious.