Learn Croatian: Čovjek treba vodu.

Voda is a feminine noun. In this sentence, it is the direct object (the thing that is needed). When a feminine noun ending in -a becomes a direct object, its ending changes to -u. This is called the accusative case, which you are practicing in this lesson!

How do we know it translates to "The man" if there is no word for "the" in the Croatian sentence?

Croatian does not have articles like "a", "an", or "the". Depending entirely on the context, čovjek can mean "a man" or "the man". In an isolated sentence like this, "The man" is the most natural way to translate it into English.

I've learned the verb "to need" is trebati. Why is it treba here?

Treba is the present tense form for "he, she, or it". Since the subject of the sentence is čovjek (a "he"), we use the matching 3rd-person singular form of the verb.

Because of the changed word ending on vodu, could I change the word order to Vodu treba čovjek?

Yes, you can! Because the -u ending clearly marks vodu as the object receiving the action, the meaning stays exactly the same even if you flip the sentence around. However, Čovjek treba vodu (Subject-Verb-Object) is the standard, neutral word order, just like in English.