I can answer this one! I would say that the during the Song Dynasty was when China's population began to increase dramatically compared to it's stagnant population in previous times. The main reason being that it was the time rice became staple in the Chinese people's diet. Rice production expanded on a large scale, it was easy to eat, nutritious, and less difficult to cook then other staple crops. It was in the Song Dynasty that there was a discovery of a new rice strain from Vietnam that was more drought resistant and faster to ripen. The south had the climate and rainfall conducive for rice production but the land was too topologically irregular and boggy to be exploited for rice farming. Agricultural engineering innovations in damming techniques, water pumping, irrigation systems, and land terracing, allow for unsuitable lands like marshes, swamps, coasts, and mountains to be utilized for rice cultivation. The Song government also implemented tax incentives to encourage these agricultural improvements.

Here's a quote on the numbers we are talking about,

"...(T)he late Tang, political fragmentation so lamented by political thinkers seems, if anything, to have stimulated economic growth. One of the clearest signs of this is the doubling of population between 750 and 1100. In 742 China's population was still approximately 50 million, the same it had been in 2 A.D. Over the next three centuries, with the expansion of rice cultivation in central and southern China, China's food supply steadily increased and so did it's population, which reached 100 million by 1100..."

"Cities in the provinces also grew at an unprecedented pace, dozens attaining populations of 50k or more. Jiankang, an inland city in north Fujian had perhaps 200k residents; Quanzhou, a coastal city in southern Fuijan, was even larger- its governor in 1120 claimed 500k residents for its city and its hinterland."

Source: Cambridge Illustrated History: China 2nd edition by Patrica Ebrey.

Wasn't there also a massive population boom after WWII, under Chairman Mao?