The phrase is often used as an idiom, not literally referring to things below the sky. There's no cure under the sun for his type of stubbornness.
Pro Tip 2/3
Emphasizing Abundance
Use it to emphasize a very wide range or large number of items, topics, or possibilities. You can find any gadget under the sun at the electronics market.
Pro Tip 3/3
Colloquial Expressiveness
It adds color to speech, making it more vivid and expressive than simply saying 'everything'. We offer every service under the sun to keep our clients happy.