Standard Mandarin vs local dialects

Standard Mandarin (普通话, Pǔtōnghuà) is taught in schools nationwide and is spoken by nearly everyone under middle age, but it coexists with dozens of genuinely distinct regional languages, or topolects — Cantonese (粤语) in Guangdong and Hong Kong, Shanghainese (上海话) and other Wu varieties around Shanghai, Hokkien/Min (闽南话) in Fujian and Taiwan, Sichuanese (四川话), and many more — several of which aren't mutually intelligible with Mandarin at all, despite sharing a writing system.

In many homes and among older generations especially, the local dialect is still the language of daily life, with Mandarin reserved for school, work, media, and talking to outsiders. Younger, urban speakers are often fully bilingual in Mandarin and their local dialect, switching between them depending on who they're talking to. In a handful of cities — Shanghai and Guangzhou/Hong Kong are the clearest examples — the local language carries real local pride and identity, and even a few words of it can land well from a learner who otherwise only speaks Mandarin.

As a learner, you'll almost always be addressed in Mandarin, and Mandarin gets you everywhere in the country — this isn't a barrier you need to solve. It does explain a few things you might notice along the way: an older relative or shopkeeper who seems to speak Mandarin with an unusual accent, or Mandarin peppered with dialect words in casual conversation, especially in the south.