I’m often asked what I mean when I refer to the Chinese language. Which Chinese? Do you mean Mandarin?, they say. Well, yes, the standard language of the People’s Republic of China is what has been referred to in the west for centuries as “Mandarin”. These days linguists just tend to refer to “Chinese”. Nobody knows where the term “Mandarin” comes from – some fondly believe it is related to the Portuguese word “mandar” (to order), probably a myth* – but it referred to the language spoken by the educated classes of Peking to rule the Empire. After the overthrow of the Manchu dynasty in 1911 the Chinese republic started to standardise some aspects of the language, especially prununciation, and Putong Hua, literally “common speech” eventually became the national language in 1932. It has been the language of education and communication ever since.
Mandarin, thus defined, is spoken as a native language by about 70% of the Han Chinese, albeit it with much dialectal variation. The rest speak other closely related languages, of which the best known are Cantonese (e.g. in Hong Kong) and Shanghainese. The Chinese think of these as “dialects”, but they are mostly mutually unintelligible and from a linguistic point of view make up a family of so-called Sinitic languages, just like the Romance and Germanic families in Europe. It seems that Cantonese and Mandarin are about as alike as, say, French and Italian, and I have met educated people from Hong Kong who understand almost no Mandarin.
Hundreds of millions of Chinese do not speak a Sinitic language at all. Their native languages belong to unrelated languages families of which the most important are Altaic in the north Tibeto-Burman and Tai in the south and Austronesian in Taiwan (not to be confused with Taiwan Mandarin!). For a detailed study, see The Languages of China by S. Robert Ramsey.
* Another theory: Mandarin \Man`da*rin”\, n. [Pg. mandarim, from Malay mantr[=i] minister of state, prop. a Hind. word, fr. Skr. mantrin a counselor, manira a counsel, man to think.] http://forum.wordreference.com/showthread.php?t=194962