This is primarily due to what "cooperatives" and communes were during the 50s. Technically the communes existed until the 80s, after which they were replaced with townships.

Cooperative in the Maoist sense are not all what cooperatives or "co-ops" imply in the West, nor were they even called cooperatives. Cooperatives made sense for China in the 1950s and were a logical response to deficiencies in the Chinese economy and infrastructure.

In 1950, the new Chinese Communist government embarked on a land reform campaign. This had a dual purpose. The first was to improve agricultural output, the second of course was to shore up support for the new regime amongst the Chinese peasantry and to eventually move China along the path to reach socialism, then Communism. Essentially, land was broken up as evenly as possible (something very difficult to do as some land is inherently more valuable than other land). Landlords, whose income often depended heavily on large numbers of tenant farmers to work the land, had their lands redistributed to their former employees. These landlords were to later become political scapegoats for all manner of societal ills for the next 20 years.

In the south of China, landlords tended to have larger holdings and more tenant farmers. In North China, landlords usually had much less land, and thus fewer tenants. This has to do primarily with issues of land quality. Agricultural productivity was much lower in North China due to flooding issues, soil quality, and a drier climate. It was more challenging for families (over a long period of time) to accumulate capital to acquire more land. This is a minor point in this discussion.

Of course, even after land reform China was not ready to fully realize its agricultural potential. The last four decades of civil war, revolution, and foreign invasion had decimated much of China's already meager infrastructure. Manpower was also an issue. Millions of people had died during the Japanese invasion and with the Korean War and Chinese involvement in it, over a million Chinese soldiers were sent to the front. Admittedly, the Korean War was not a huge manpower drain given how large the Chinese population was in the early 1950s. The 1953 census puts this figure at 582.6 million. The final problem was that equipment availability was poor and quality was low, the modern agricultural tools commonplace in the West were expensive to import and impossible to produce domestically. Things like motorized farm vehicles and chemical fertilizer were not an option. People still pushed/pulled their own plows, unless they were lucky enough to have a beast of burden.

The Maoist solution to this issue was to create these mutual aid teams. You don't have an ox to pull plow but your neighbor does? Ok, so you help your neighbor out with harvesting his fields and he'll lend you, and the entire community, his ox. Communities would work together to maintain fields, harvest, plow, make fertilizer, kill pests etc. This helped agriculture, and the Chinese economy, recovery extremely quickly. It's no wonder that these years were viewed so fondly for so long, even with an ongoing war with the world's most powerful empire.

Of course there were some challenges in implementation. Wealthier peasants did not want to join the cooperatives, why would they want to share their valuable resources with those who had little of value to contribute? Poorer peasants were sometimes barred from joining the teams as well.

"The cadres and the peasants are advancing under the leadership of the Party and, fundamentally, the movement is healthy. In some places they have made certain mistakes in their work; for example, poor peasants have been barred from the co-operatives in disregard of their difficulties, while well-to-do middle peasants have been forced into the co-operatives in violation of their interests. These mistakes should be corrected by educating the cadres and peasants and not by simply dressing them down. Blunt reprimands solve no problem." -Mao Zedong in 1955

Participation was mandatory, and over the years everyone was forced into line. It's debatable to what extent the mutual aid teams actually contributed to the agricultural and economic recover of China in the 1950s. Peace more likely had more to do with this any of the socialist reforms.

Now as for the communes, they were very different beasts altogether. This project began in 1958 and was accelerated during the Great Leap Forward (1958-1962), during which 30 to 45 million died. The communes were often massive communities were people lived, worked, and ate together. Communes differed substantially. While in some communes people lived in communal housings, in most people were allowed to stay in their homes. Private property was abolished. This meant animals and land were appropriated by the commune. In some communes, people were not allowed to keep utensils and woks to encourage people to eat at the commune canteens. The cooking implements were either used by the commune itself or, more often, fed into the new backyard furnaces to produce steel, which was almost always low quality.

There's a certain amount of debate as to why the communes failed so miserably. Since you asked about the communes themselves and not the Great Leap, I won't get into that. For that, I would suggest referencing Yang Jisheng's Tombstone. I warn you though, it is not easy to read and contains some extremely disturbing accounts of the the Great Leap Forward.

The communes failed, first and foremost, because of the implementation of pseudo-science agricultural techniques, largely influenced by the Soviet "scientist" Trofim Lysenko. The techniques used included close cropping, deep plowing, fertilizer concentration, among others. All of these failed to produce more grain and dramatically decreased output. Irrigation projects were also undertaken by communes, often unsuccessfully and poorly planned. There were few engineers in China sufficiently trained to take on complex, large-scale projects. Many of these new irrigation canals, dams, etc. failed to last more than a few years and unknown thousands died working on these projects. Labor was also issue. Many workers were forced to work on these irrigation projects or in the backyard furnaces, in some places there simply was not enough labor to maintain agricultural production.

As agricultural production fell, communes kept reporting massive spikes in productivity to gain favor with their superiors. These were often termed "satellites." Those who did not report massive gains were often punished, sometimes physically, by their immediate superiors. Some of these objecting officials, who were usually deemed to have "bad class backgrounds" or to be "rightists," were actually killed. The central government took these increases in productivity as a good sign and accelerated efforts to reach communism in 1959. To make matters worse, between 1958 and 1960 China continued to export grain, in part to pay off their debts to the Soviets. This led to three years of man-made famine. Estimates of the total death toll range from the low 20s to 50 million plus. It's now accepted that at least 30 million died, but we will likely never know the full extent of the death toll.

For more information:

Yang Jisheng's, Tombstone Cao Shuji, The Great Famine: China's Population in 1959–1961, I think this one is only in Chinese but there may be a translation out there. I know Dikotter uses Cao's work. Frank Dikotter, Mao's Great Famine: The History of China's Most Devastating Catastrophe, 1958–62