An experimental language is a constructed language designed for linguistics research, often on the relationship between language and thought.
One particular assumption having received much attention in fiction is popularly known as the Sapir–Whorf hypothesis. The claim is that the structure of a language somehow affects the way its speakers perceive their world, either strongly, in which case "language determines thought" (linguistic determinism), or weakly, in which case "language influences thought" (linguistic relativity). (For a list of languages that are merely mentioned, see the relevant section in List of constructed languages.)
The extreme case of the strong version of the hypothesis would be the idea that words have a power inherent to themselves such that their use determines not just our thoughts, but even that which our thoughts are about, i.e. reality itself.