This world was ruled by a cabal of three powerful disembodied brains called the Providers. The Providers' society revolved around betting their monetary reserves (counted in a currency known as a quatloo) on various aspects of captured slaves' ("thralls") lives, including open combat with one another. The thralls lived in a compound on the lower hemisphere of the planet.
The Federation starship USS Enterprise under command of Captain James T. Kirk was obligated to visit the planet to secure the release of several crew kidnapped by the Providers. Upon arrival, the Enterprise discovered numerous species enslaved on the surface as thralls, including their missing crew. Eventually, to free the thralls and his crewmates, Kirk entered into open combat against three drill thralls, betting not quatloos on his victory, but the condition of freedom for all if he was victorious, or enslavement of the Enterprise crew if he lost. He won, and the Enterprise left the system shortly afterward.
The "Triskelion symbol" was designed by Matt Jefferies. (Star Trek Sticker Book, pg. 22) A bottle with a Triskelion emblem said to be used in several Star Trek: Enterprise episodes including "Rajiin" was sold off on the It's A Wrap! sale and auction on eBay. 
According to Star Trek Maps (p. 27), Triskelion was the second planet in the system. When the small and disparate humanoid colony was given self-government it had a population of 480.