In the West (at least in the US), there is a common stereotype that Chinese culture is very uniform. What's more surprising is that I have met a number of Chinese people who have a similar perception. They generally claim that all Chinese people speak different dialects of the same language, point to the common writing system, and argue that ethnic differences among the various "Chinese" ethnic groups are fairly superficial. Seemingly counter to this, many linguists argue that the Chinese language varieties have more variation than Romance languages, and they point out that the shared writing system does not work well without modification for non-standard varieties. Additionally, my superficial understanding of China is that there is pretty large cultural and ethnic variation across China. Where do these ideas of uniformity come from? Are they grounded in reality, or are they perhaps intentionally constructed?
Notions of Chinese uniformity in China are very recent — I would say late-Qing or early-Republican era (1880–1920). For thousands of years, of course, people living in China were aware that there were shared Confucian practices and ideologies sanctioned by the imperial authorities, and that imperial officials spoke a version of Chinese called guanhua (lit. ‘the language of officials’). But by and large, people didn't travel far from their places of origin, and there was little sense of being “Chinese”. For the most part, people identified with their own local languages and families; the “Han” ethnic marker was not particularly salient, and no one spoke guanhua as their first language (it wouldn't make sense).
It was only in the late-Qing era, under the threat of imperialism, that intellectuals began to construe China as a unified ethnic Han state. In part, this was an effort to paint the Qing Manchu rulers as foreign invaders and occupiers. A unified China was also seen as the key way to save it from being dismantled by imperial powers — intellectuals looked to Meiji Japan as a model, which had successfully (on the surface) unified the state in a few short decades after the Meiji Restoration (1868).
The Qing imperial court also played its part in entrenching the notion of a unified China in an effort to save itself. Obviously it did not paint the imperial family as foreign invaders, but it did institute a guoyu (lit. ‘national language’) based on guanhua, and also promulgated a Nationality Law in 1909. For the first time in Chinese history, the entire Chinese state was called to speak a common language, and the notion of a “Chinese national” was legally created.
Hence, in the early 20th century, people began to talk about 救國 jiuguo (‘saving the country’) not only in the sense of saving the government and the regime, but also in the sense of saving a nation of people. But it is important to remember that this idea of a unified China took time to develop. As late as the Sino-Japanese War of 1894–5, Chinese soldiers were still far more loyal to their provinces or even localities of origin than to a wider “China”. The disunity of the Chinese army was a major reason for their defeat at the hands of the Japanese.
TL;DR: The notion of Chinese cultural/linguistic/ethnic uniformity is very recent. Though notions of shared practices and traditions had existed for thousands of years, people only began to think of themselves as being part of a Chinese nation speaking a common language in the late-19th and early 20th-century.