Accusative case is the case of noun used to mark the direct object of a verb.The direct object of a verb is the thing being acted upon (i.e., the receiver of the action).
EX: You(subject-in fact agent but that is about something else) drink(verb) the water(direct object). Sen(subject) suyu(direct object) içersin(conjugated verb((yüklem))).<pre>
You(subject-agent) sold(verb) her(indirect object) the book(direct object). Sen(subject) kitabı(direct object) ona(indirect object) sattın(conjugated verb). I(subject) love(verb) you(direct object). (Ben)(subject) seni(direct object) seviyorum(conjugated verb). Play(subject) the guitar(direct object). Gitarı(direct object) çal(conjugated verb).</pre>
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If you have just talked about some water, you can identify it with "the water" afterwards.
For example, if someone offers you either a bottle of water or a bottle of juice, you can say, "I will take the water".
"Suyu içerim" is not "I drink water" but "I drink the water" -- perhaps because you had been talking about the water that is always in the fridge for guests.
It can't be sui because of vowel harmony: the accusative suffix will be one of ı i u ü depending on the last vowel of the word.
Since su ends in u, it can't be i but is u.
But it's not suu because Turkish generally doesn't like two vowels next to each other -- so you need a buffer consonant -y- before the accusative suffix.
suyu can be "his water" but remember that possessed things are definite -- so if they are the direct object, they take the accusative case, and you get suyunu.
Thus this can't be "his water" but just "the water", i.e. su + accusative case ending rather than su + possessive ending + no case ending.
(It's irregular; the accusative is suyu rather than *susu.)