The Family Church (also known as the house churches or underground church) is made up of unregistered assemblies of Christians, which operate independently of the Chinese government sanctioned Three Self Patriotic Movement. (TSPM)
During the Cultural Revolution, 1966 to 1976, religion in China was effectively banned, including even the TSPM which had been formed shortly after the People's Republic of China had been established. During that time only two to five people could gather together. All Christian worship was forced underground and the House Church phenomenon began and rapidly grew under years of acute persecution. Estimates of those killed for their faith go into the millions.
China opened to the west in 1973.
China's ruling Communist Party China is officially atheist. It's stand against the unregistered churches is also derived from a fear that uncontrolled gatherings may lead to social disorder and could evolve to mass mobilization of believers.
This is an understandable concern given the decades of strife and civil war suffered prior to forming a unified People's Republic of China.
One of the most well-known Christian leaders in China, Pastor Lin Xiangao (known to many as Samuel Lamb), was known to have said that the more the church suffers, the more it grows. “More persecution, more growth,” he told them, using his own church as an example of this truth. “Each time I was taken into prison, the church grew.”