If the birthrate in a country is too high, there will be many children, which will lead to a population explosion and a very rapid population growth - which may not be sustainable in terms of space or resources necessary. Hence a government might decide to introduce an anti-natalist policy to bring the birth rate down.
The population in China was growing at a rapid rate, and the aim of the policy was to reduce the growth to stabilize the overall population number.
The governmental policy introduced benefits for those with only one child (extra month of wages over the year, pension benefits, a house provided, free education for the child) and penalties for those with more than one child (no free education, no allowances, no pension benefits, demotion at work, payment of a fine). Other elements of the governmental police were that the marriage age increased to 20 for women and 22 for men, couples had to have permission to marry and have a child and family planning became available at work.
Did this work? The population growth has slowed, but gender selection has meant that in some regions, there are far more boys being born than girls (Shaanxi province at one point had 145 males born for every 100 girls), which leads to large numbers of unmarried men. The baby boom of the 1950s means that China’s population is now ageing.
The policy has now become less restrictive - it is now a two-child policy for most areas of the country.