What does the term "Chinese" mean? The Wikipedia article on Chinese says that many varieties of Chinese are mutually unintelligible. That is, I can't just learn "Chinese" and speak "Chinese" with anyone living in China or Taiwan.

What does the term "Chinese" mean? What makes a variety of Chinese count as Chinese, and what makes a non-Chinese language count as non-Chinese?
user3306356 provided a good answer for the language, but you need to know that written Chinese and oral Chinese can be quite different.


  A Mandarin speaker might say yī, a Cantonese jat1, and a Hokkien chit, but all three will understand the character 一 "one". -- from Wikipedia


Also I want to answer more on the Cultural aspect. For Chinese as in Chinese people, that's really complicated.

Historically, the Chinese culture influenced many others such as Japanese, Korean, Vietnamese, etc. so you may see Chinese characters, traditional clothing and buildings in their culture. The modern China split into different "areas" (I can't say country because it surely will stir up a political debate), mainly mainland China and Taiwan which ruled by 2 different political parties, the Communist Party from mainland calling itself the "People's Republic of China" and Kuomintang (the Nationalist Party) stayed in Taiwan calling themselves the "Republic of China". There are also Hong Kong and Macau, I recommend to watch "Are Hong Kong &amp; Macau Countries" on YouTube for a better understanding. These four areas have different cultures while the core is the same. Most Chinese there use Mandarin while "dialects" are also used (some see those dialects as separate languages. Spoken Cantonese being one which used by people from Hong Kong, Macau and many from southern China.) There are also Tibet and other "minorities" which got their own dialects/languages.

For "some" ("many" depends on your view) people from Tibet, Hong Kong, Macau and Taiwan, they think they are culturally different and should be called differently (e.g. Hongkonger, Taiwanese), so Chinese, AFAIK, are mainly refer to mainland Chinese while it can also refer to ethnic Chinese in some occasions.