According to Northall author of "English Folk-Rhymes" (1892), when you recite this rhyme: "It is usual to tap the feet of children in imitation of shoeing a horse."

Robert Barnes, Fellow Fine - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

*The "horse is shod" means the horse's shoes have been put on.

The Real Mother Goose (1916) has the first line as, ""Robert Barnes, my fellow fine..."

Here's a slightly different version from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith:

"Robert Barnes, fellow fine,
Can you shoe this horse of mine?"
"Yes, good sir, that I can,
As well as any other man:
Here a nail, and there a prod,
And now, good sir, your horse is shod."

Thanks and Acknowledgements

This rhyme can be found in The Nursery Rhyme Book, edited by Andrew Lang and illustrated by L. Leslie Brooke (1897). This rhyme and illustration can be found in The Real Mother Goose (1916), illustrated by Blanche Fisher Wright.