"The man eats dinner."
Translation:Bărbatul mănâncă cina.
It's like this. For lack of a better explanation, see "cina" as something particular that the man is eating. E.g.: you have dinner only once during a day as opposed to, say, fish which can use both the definite and the indefinite article, with similar meaning as in English:
He eats fish. -- Mănâncă peşte.
He eats a fish. -- Mănâncă un peşte.
He eats the fish. -- Mănâncă peştele.
Btw, in real life, say if your mother were to ask you "Did you eat/have dinner?" she would say "Ai mâncat de seară?" -- "Have you eaten for the evening?". "Ai mâncat cina?" or "Ai cinat?" sound odd.
Duo has a propensity for literal translations which makes it easier for beginners to spot the one-to-one mapping of the sentence structure.