> One having exceptional qualities or potential but lacking refinement or polish
> Something that is in poor condition but that is likely to become valuable with appropriate care or attention
This idiomatic expression is obviously a metaphor for the original unpolished state of diamond gemstones. It comes from the fact that when diamonds are newly mined – that is, before they have been cut and polished – they don’t shine, in fact they look quite a lot like pebbles and are easily overlooked in their “rough” state.
Example
He looks a little messy, but he’s a diamond in the rough
Her singing voice is beautiful, but she needs help with her gestures; she’s a rough diamond