"Chinese" is really just an overall term for a language(s) spoken in China. It is not a language.
There are hundreds of languages in China.
There are two more well known one:
Mandarin - This is spoken all over pretty much all over China, and the Chinese translation for this means 'standard language'. Generally if someone says they can speak 'Chinese', this is what they are referring too.
Cantonese - This is the language spoken in Hong Kong and the area of the South East (Guangdong). It's has lots of similarities to Mandarin, and a Mandarin speaker may be able to understand a bit, but won't be able to speak it themselves.