This is the American name for a little children's singing game. Kids hold hands, walk or skip in a circle, sing, and then all fall down. The song goes something like: Ring-around-the-rosy, pocket full of posy, ashes, ashes, we all fall down. In Britain the same kind of game is Ring a ring o' roses, and they often sneeze (atishoo) before they fall. Though actually, a lot of grown-ups like to say the song is about the plague — a rosy rash, flowers to hide the smell, then falling down for death. Many scholars think that story came later, and that it was just a dancing game; we do not know for sure. You will see the name with hyphens in some books and as separate words in others. It is playground language, not classroom-formal.