"I do not want that orange."
Translation:O portakalı istemiyorum.
Because it's a definite direct object, so it needs the accusative case.
It's the direct object of "istemiyorum" (it's the thing that is not wanted).
And it's definite because of the "o" ("that") in front -- demonstrative determiners such as "this, that" always make the thing they stand in front definite.
So since it's a definite direct object, it needs the accusative case and the ending -(y)i.
Because of that ''that'',it shows you which orange,not just any other orange.