"Marcus studies Latin."
Translation:Marcus linguae Latinae studet.
studere is a verb that normally takes the dative. There are a few verbs like this, if I am not mistaken it is because they are actually intransitive, but they will sometimes have translation to transitive verbs. studere can also be translated as 'to be eager for', 'to strive after' ('to study' being a later usage from my understanding).
I simply used 'direct object' to simplify the concept, and also why I but it between apostrophes.
Information on studere: http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0059:entry=studeo
Information on verbs that take the dative: http://dcc.dickinson.edu/grammar/latin/dative-special-verbs
Calling it "direct object" is confusing & unclear because the very definition of accusative is "direct object" and the very definition of dative is "indirect object".
I found it much more clear when you said studere is intransitive, thus needing an indirect object.
Here is an analogy. "Marcus studies for accomplishments in the latin language" is something an old-fashioned English speaker might say (picture a Jane Austen novel), and may be in the spirit of what studere means.
The direct object (the accusative part) is "for accomplishments"... but it is so obvious that English speakers stopped including it. That leaves us with the indirect object (the dative part), "Marcus studies in the Latin language".
Americans then went further, going to "Marcus studies the Latin language" and finally just "Marcus studies Latin", transforming it to the accusative (direct object). But that's an American problem ;)
To come back to the main example: the area of study really is an indirect object; meanwhile a direct object is unnecessary and is omitted. Something like that, I think, happens in the Latin - hence the dative.