They are an group of people who believe that the benefits of breathing exercises are more beneficial to health than the risk of being tortured by Chinese officials for believing it.
Falun Gong has an odd history.
It was formed as a health activity in China, and made public in 1992. Communism was discredited and collapsing and the new economy was forming, but there was no opportunity for the older generation, who had spent most of their lives forced to believe in communism as a life goal, but were too old, and mostly too uneducated to participate meaningfully in the new economy. People needed something new, something they could believe in which wasn't the greater glory of the Chinese Empire. Getting together in groups and doing breathing exercises was a way for the older people spend their time, to socialize, and also to relax and concentrate on their health. Focusing on something which promoted health, honesty and tolerance was also a welcome change from focusing on the Chinese leadership.
Initially the Chinese government encouraged it. Having their people concentrate on something which promoted health, honesty and tolerance seemed harmless enough. Unfortunately it became just a little bit too popular for the comfort of the power bloc.
Around the turn of the 21st century, Falun Gong claimed to have about 100 million members (one 13th of the population of China). While this may seem to be stretching credibility for an organization which promotes honesty, the fact remains that there were a large number of followers - possibly as many as the the members of the Chinese Communist Party (the outer rings of the power bloc which control China).
The power bloc could not afford to have any organizations with more people (and therefore more democratic integrity) than the Communist Party.
The Chinese were still reeling from the international face-slap from their Tienanmen Square massacre. They knew they could massacre several hundred people in Tienanmen Square, and write them off as counter-revolutionaries, however they had watched what had happened with the 'People Power' revolution in the Philippines, where millions of people hitting the streets and chanting slogans brought down the corrupt Marcos dictatorship. They knew that even 10 million people walking the streets shouting ''corrupt commies out!' would bring down the Chinese government. It takes a lot of tanks to crush 10 million people.
The Chinese government faced the choice of crushing Falun Gong or facing a revolution (or counter-revolution as they would call it). They denounced Falun Gong as an 'evil movement' and began to prosecute its followers.
Oddly enough their actions have provided their own justification for them. Clearly some people in China are still practicing Falun Gong, and one has to ask why. Few rational people would believe that the health benefits from breathing and moving exercises could outweigh the risk of being tortured and raped by Alsatian dogs in a Chinese prison.
The conclusion must be that most of the Falun Gong members (at least in China) are be motivated by desire to protest about the Chinese government. Of course if this group grows too big, this creates a credibility problem for the Chinese government - they can't claim to be acting for the people in the face of a large protest group. Hence it is critical for the Chinese government to limit the size of Falun Gong. Which they do by imprisoning and torturing their members, and by spreading propaganda about the Falun Gong being an evil cult which murders and eats babies or whatever.
Occasionally Westerners (including some moronic Australians) go to China to protest in Tienanmen Square. They get beaten up by Chinese authorities and sent home. It is hard to be sympathetic to anyone in this situation.