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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?
Mou某 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 yāt, a Shanghainese iq, and a Hokkien chit, , but all four will understand the character <一> to mean "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 & 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 the term "Chinese", AFAIK, mainly refers to mainland Chinese while it can also refer to ethnic Chinese in some occasions.
I would say, so-called, Chinese is what we would call Modern Standard Mandarin (MSM) but can also include all dialects/topolects.
Although there should be a standard, it seems that all dialects/topolects (i.e., any language spoken in China and its territories — no matter its origin) can be considered Chinese "languages".
Chinese, in general, should just be the same as Mandarin. Whereas Chinese languages could include any language spoke in China and all of its territories.
Depending on the time in history, the consistency of "Chinese" varies. Today, the name "Chinese" represents people who came from 6 ethnic groups, each has its own speaking language, and a few of them have their own written language, but are longer in daily use except "漢字".
Other than the different speaking languages among the ethnic groups, due to geographic segregation and other factors, there are many dialects in each ethnic group as well, which had even prevented a person to comprehend the expression of another person from the neighboring village.
Then, how do the "Chinese" communicate with each other? Simple, use the official language - "Mandarin", which is taught everywhere around the world. Then you can speak/talk to every Chinese trouble-free in mainland China and Taiwan.
You are making it a bit complex. Chinese is a language that Chinese people speak. The standard Chinese is called mandarin or 普通话。Besides mandarin, there are many dialects in Chinese.
