I began peeling oranges this way when I was a teenager. It was partly for the cooking possibilities and partly for the clean fingernails and partly because it’s wonderful as a party trick.
Someone showed me it as a way of creating bowls from the skin of the fruit. Perfect for fruit jelly and ice cream and putting back together and into the fruit bowl so that someone grabs at a fruit and finds a mere shell. Not that I would do something that wicked. Not past my teen years, anyhow.
The method is really straightforward. You use a single tine (or prong, if you’d rather call it a prong) to cut just below the skin, halfway between the two ends. You want to cut through the pith, but not enter the flesh at all. It should be a perfect circle and meet itself when you finish.
Then you turn the fork upside down and use the other end as a lever. Enter through the cut you just made and gently push it further and further around the orange, just under the skin.
When you’ve liberated the orange from the skin, it will just come off.