Because of a number of technological discovery and diffusion events that significantly increased agricultural output all around the world that all get grouped under the label "Green Revolution." A lot of these technologies were already taking off in the 50's and 60's.

Consider how China has accommodated an enormous swelling of its population in the second half of the 20th century. The 1953 PRC census counted about 580 million people. The 2000 PRC census counted almost 1.3 billion people. Between the years of 1930 and 1950 or so China was already pushing up against a Malthusian limit. Traditional agricultural technology based on manually powered terracing, irrigation, lime and animal fertilizer, crop rotation, and crop breeds was reaching its production frontier. Further gains in output due to commercialization and comparative advantage in utilization of farmland was also reaching its limits. Traditional Chinese agriculture was, by pre-industrial standards, enormously productive measured by output per area, but by the 30's radically new technology was needed to advance further. During this time a large proportion of peasants were severely malnourished, falling below the recommended minimum 2000 kcal / day.

Starting in the 50's however a number of technologies diffused throughout the Chinese countryside that broke previous barriers to increased output. One was powered irrigation, which drove a massive increase in irrigated acreage, rising from about 16 million ha in 1952 to about 38 million ha in 1978 (there was a plateau but since the 90's there has been a continued but slower increase). Also important were the advent of deep pumps that for the first time reached aquifers 30 m underground, allowing the irrigation of farmland far away from major sources of surface water. Prior to the advent of powered pumps, irrigation was driven by man powered pump and chain systems or simply by buckets balanced on a person's back, while unirrigated farmland simply depended on unreliable natural rainfall.

Second, there was a massive increase in chemical fertilizer production combined with new crops specifically bred in labs to complement modern fertilizers. In 1952 nitrogen fertilizer usage was practically nonexistent in China, but rose to over 40 million tons by 1995. Fertilizer was meant to complement modern seed varieties that were being systematically bred to produce high yields. In 1964 Chinese scientists developed a high yield variety of dwarf rice. In 1961 scientists introduced high yield hybrid corn (with the downside that they were sterile). Hybrid rice was introduced in 1976. By the mid 90's the vast majority of farms were using high yield varieties. Starting in the 90's, GMO research also started taking off, but this is past the 20 yr limit.

Technology of course isn't the only contributing factor to output growth, output depends on institutional factors that allow areas to specialize to local conditions and trade with one another, that allow the investment into capital like pumping stations, that disseminate hybrid seeds, etc. There's been a lot of research into the contributions of various factors to increased output and a lot of resulting debate. I'm discussing technology only since the institutional factors unique to China aren't applicable to the rest of the world. Well, aside, from the Smithian efficiency generated by globalization. See:

Technological change: Rediscovering the engine of productivity growth in China's rural economy, Huang, Rozelle

Technological Progress and Chinese Agricultural Growth in the 1990s, Liu, Yunhua, Wang

Evolution and Diffusion of Agricultural Technology in China, Stone

Commercialization and Agricultural Development: Central and Eastern China 1870-1937, Brandt

The Peasant Family and Rural Development in the Yangzi Delta, 1350-1988, Huang

The Chinese Economy: Transitions and Growth, Naughton

EDIT: should point out some ongoing debates between scholars cited here. Studies on the pre-war economy differ on the level of poverty in the countryside and the direction of development. Studies on the post-war economy differ on the contribution of market efficiency vs technological efficiency in output growth.