It's mostly a children's song used to teach counting. The literal meaning of the song is less important for English-speaking children than the rhyming scheme and counting. According to the Wikipedia page, the oldest version of the rhyme has to do with a little boy "playing nick nack" on his thumb, which means tapping out a rhythm. "My name is Jack Jintle, the eldest but one, And I can play nick-nack upon my own thumb. With my nick-nack and click-clack and sing a fine song, And all the fine ladies come dancing along." It's been suggested that the more common version, the one you're quoting, has to do with an old man who picks up garbage using a sort of wheel-barrow. So when it says "paddy-whack" it refers to him slapping or hitting his wheel-barrow. And, of course, "rolling home" would be him literally rolling his wheel-barrow of trash home to sort out and sell later. All that being said, as a child, I remember quite a few drawings that had an old man literally curling into a ball and rolling down the road, and next to none with a man and a wheel-barrow. That's not to discount the definition offered (which seems sensible enough to me), but to reinforce the fact that most English speakers (in America anyway) take the song as mostly nonsense, similar to Dr. Seuss (a famous children's author).

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