It is the language of the Sindar?, the elves who remained in Beleriand? and waited for Thingol?, when he had disappeared.
The language was described briefly in an appendix, and probably in more detail in other works. There are people who claim to be able to read and write this language, so perhaps it has become a real-world language after a fashion.
Quenya, the language of the High Elves (particularly the Noldor) was designed to be a little bit like Finnish, and the two were made as if they evolved from a common ancestor. But Sindarin reflects different aesthetics.