An unpolished object has a dull or matte surface, rather than a shiny one. An unpolished person, on the other hand, is socially awkward or unsophisticated.
The gravel in a parking lot is unpolished, while the marbles you collect in a jar are highly polished and shiny. When you use this adjective to describe people and the way they act, they're lacking a figurative kind of polish instead. An unpolished speech wasn't practiced and perfected but is improvised and rough. Unpolished behavior at a fancy restaurant might embarrass the other diners (especially if it involves belching or feet on the table).