Because this sentences is in Akkusativ and the apple has male gender. So ... Nominnativ Akkusativ Der Apfel = Den Apfel When you use the verbs Essen , trinken , rauchen .... the sentence is in Akkusativ

As Laura has said it, it's accusative case of the male definite article 'der'. I can just add that accusative (Akkusativ) roughly corresponds to direct objects of English transitive verbs (like her in 'he loves her' ) - and that's true for all languages by the definition of accusative. Not really always it corresponds well, but the idea is clear: you eat the apple. Not 'of the apple' or 'to the apple' or 'by the apple' etc. So, accusative.

"den Apfel" is in the objective (accusative) case, causing the article "der" to change to "den".