Wallflowers are wildflowers in Ireland.

 

This video explains how to sing the song (and how to sing in general). You can find the version of the song that's sung in the video in the notes.

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Notes

Here's another version:

Wall flowers, wall flowers,
Growing up so high,
He had the measles
He'll never ever die.

*****

Here's another version as submitted by Miss H. E. Harvey of Howth, Dublin to "The Traditional Games of England, Scotland, and Ireland" (1898) edited by Alice Bertha Gomme:

Wall-flowers, wall-flowers,
Growin' up so high,
Neither me nor my baby
Shall ever wish to die,
Especially [girl's name],
she's the prettiest flower.
She can dance, and she can sing,
and she can tell the hour,
With her wee-waw, wy-waw,
Turn her face to the wall.
(Or "Turn your back to all the game.")

Game Instructions

The children form a ring by joining hands. They all dance slowly round, singing the words. When the one child is named by the ring she turns round, so that her face is turned to the outside of the ring and her back inside. She still clasps hands with those on either side of her, and dances or walks round with them. This is continued until all the players have turned and are facing outwards.

Photos & Illustrations

Thanks and Acknowledgements

Photo from Wikipedia. Diagram of how to play the game comes from "The Traditional Games of England, Scotland, and Ireland" (1898) edited by Alice Bertha Gomme.