The Sapir-Whorf Hypothesis (SWH) is a hypothesis in linguistics, stating that there are notable differences in thought patterns of speakers of different languages, and that the way people's brains function is strongly affected by their native languages. It's a very controversial theory, championed by linguist Edward Sapir and his student Benjamin Whorf.
First discussed by Sapir in 1929, the hypothesis became popular in the 1950s following posthumous publication of Whorf's writings on the subject. In 1955, Dr. James Cooke Brown created the Loglan language (which led to the offshoot Lojban) in order to test the hypothesis. After vigorous attack from followers of Noam Chomsky in the following decades, the hypothesis is now only believed by linguists with a grain of salt; that thought processes are somewhat affected by language, but that differences aren't that notable.
Central to the Sapir-Whorf hypothesis is the idea of linguistic relativity: distinctions of meaning between related terms in a language are often arbitrary and particular to that language. Sapir and Whorf took this one step further by arguing that a person's whole world view is determined by the vocabulary and syntax available in his or her language.
The extreme ("Weltanschauung") version of this idea, that all mental function is constrained by language, can be disproved through personal experience: people in every language occasionally struggle to express their exact thoughts, feeling constrained by the language. It's common to say or write something, only to correct one's self or further clarify meaning, especially to someone being explained to. These show that ideas are not merely words, because one can imagine something without being able to express it in words.
The opposite extreme - that language does not influence thought at all - is also widely considered to be false. For example, it has been shown in studies that people's discrimination of similar colors can be influenced by their vocabulary for distinguishing said colors. Another study showed that deaf children of hearing parents are more likely to fail on some cognitive tasks unrelated to hearing, while deaf children of deaf parents succeed, due to parents being able to more extensively communicate. Computer programmers who know different programming languages often see the same problem in completely different ways.
The Neuro-Linguistic Programming (NLP) analysis of the problem is direct: most people do notable thinking by talking to themselves and by imagining images and other sensory phantasms. To the extent that people think by talking to themselves, they are limited by their vocabulary and the structure of their language and linguistic habits. (However it should also be noted that everyone have idiolects, mental language patterns individual to them.)
John Grinder, a founder of NLP, was a linguistics professor who perhaps unconsciously combined the ideas of Chomsky with the Sapir-Whorf hypothesis. A seminal NLP insight came from a challenge he gave to his students: coin a neologism to describe an idea for which you have no words. Student Robert Dilts gave an example by coining a word for the way people stare into space when they are thinking, and for the different directions they stare. These new words enabled users to describe patterns in the ways people stare into space, which led directly to NLP results — as notable a validation of the weak hypothesis as one could ask.
Lojban is thus designed to test the Sapir-Whorf hypothesis, by attempting to expand the speakers' minds and express thoughts as conveniently as possible to see if there's any notable effects in the speakers' thought patterns/worldview. The only complication with this is that the third factor - the speakers all wanting to learn Lojban, an obscure language - could skew the results somewhat, but the only way to fix that is to get more Lojban speakers.