Not much is known about the Cheetah People as people who encounter they rarely live long enough to tell anyone. They are essentially a fun-loving species who have the ability to travel to other worlds to capture prey. Although they can transport prey back to their planet they are unable to carry prey away from the planert.
When hunting they often used Kitlings to locate prey on another planet and then transport themselves to the planet where they would capture the prey.
Being humanoid they are not able to run as fast as Earth Cheetah's, and often capture their prey on horseback. Whereas their planet is able to possess people and slowly transform them into a Cheetah Person, an individual is able to possess a human, and only a strong mind can resist the process. When the Doctor and Ace encountered the Master on the Cheetah Planet the Master was able to use a friend of Ace, Midge, to return to Earth, and the Doctor was able to use Ace to do the same thing.
The Cheetah People had a strong bond with their planet. When food was scare they would fight each other, and these fights were triggering explosions that were slowy tearing the planet apart.