。
Her manners are extremely refined.
Literal
She [topic-は] manners [subject-が] extremely refined is.
極めて ('extremely, exceedingly') is a literary intensifier, more elevated than the everyday とても. 上品 ('refined, classy, elegant') often appears as a compliment about taste, manners, or breeding. The opposite is 下品 ('vulgar, crude'). である ('is,' the literary copula) cements the formal register — this is the language of profile pieces or character descriptions. The frame X は Y が Z だ — topic, subject of the comment, predicate — is canonical Japanese.