(written from a Production point of view)
The term felinoid was descriptive term used to describe a species that evolved from feline origins, and retain cat-like physical traits as opposed to primates, who followed a primate evolutionary pattern, or insectoids, who were descended from insects.
The Star Trek Concordance (1st edition, p. 158) defined the species as "a cat-type intelligent being. In the case of Lieutenant M'Ress, she walks on two legs like a humanoid, but has a distinctively feline face, ears, paws, and tail." Aside from the Caitians, the Concordance also liken the Kzin and the Vedala as felinoids; likewise, the "Cat Woman" seen in Star Trek V: The Final Frontier would also fit this definition.