A string of impossible ifs, wishing beggars into riders and turnips into watches, that lands on a proverb about wishing rather than doing. Older children tend to get more out of the joke than younger ones.
From Mother Goose / Nursery Rhymes (traditional). See the whole collection.
If wishes were horses, beggars would ride.
If turnips were watches, I would wear one by my side.
And if "ifs" and "ands"
Were pots and pans,
There'd be no work for tinkers!
About this rhyme
Text: "If turnips were watches" (no mention of 'pocket'); final line is "There'd be no work for tinkers", with no stated reason.
"If wishes were horses, beggars would ride" is a well-worn English saying, turned here into a short rhyme. It pokes gentle fun at wishing instead of doing: if wishing worked, turnips would be watches, and there would be no work left for tinkers.
Public domain. Text from The Real Mother Goose (Blanche Fisher Wright, 1916), via Project Gutenberg. View the source edition