Have you eaten dinner yet?

Literal

Dinner [topic-は] already eat-[polite-past-ましたか]?

A textbook もう-question: もう ('already') combined with the past tense ~ましたか asks whether an action has been completed. 夕飯 is more casual than 夕食 (both mean 'dinner/supper'), slightly warmer and more homey in feel.