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They were introduced in DC's weekly comic series 52. Several of the characters are based on Chinese mythology.
When Mao Zedong took control of China during the Cultural Revolution, one of the first things his party did was execute any super heroes or vigilantes in China. Many escaped to the west. But after Mao's death, his party soon realized that they did not have any superpowered protectors of their own to counter those of other countries.
They soon searched for any metahumans in China. Superheroes were dubbed 'super-functionaries' and they formed the Great Ten from China's greatest powers, although they all weren't necessarily heroes. The first four members of the team were created when the Chinese government captured a Durlan space craft. With this alien science, the reverse engineered technology to make the Immortal Man in Darkness, the Shaolin Robot and the Socialist Red Guardsmen. August General in Iron was saved from death by a Durlan virus when his team captured the ship.
The team is lead by August General in Iron, and the team is to follow all orders from the Chinese government, which doesn't always include heroic acts, but mostly what is in the best interest of the Communist party. For example, in the story arc "World War 3" in which Black Adam basically went mad, when Hal Jordan and Guy Gardner of the Green Lantern Corps flew into China's air space the Great Ten assumed they were a threat and attacked them.
Their base is actually located inside of the Great Wall of China, sort of as an extension of it.