Translation:I understood this example, but I do not understand the subject exactly.
I'm not sure I understand your question exactly ;-)
If you're asking why you can't leave "the subject" out, it's because it is a different object than the one in the first clause: We understand the example, but not the subject.
If that period was a typo and you're questioning the word order: "I do not understand exactly the subject", this is incorrect because we cannot separate English verbs from their objects. The adverb must come before or after both:
"I do not understand the subject exactly." OR "I don't exactly understand the subject." :-)
I've certainly heard past tense ("anladım") used where English would use present tense ("I understand"). Or in question form: "Anladın mı?" ("Did/do you understand?") It confused me the first couple times, but I started to realize that happens with a few verbs in Turkish. :-)
My guess (someone correct me if I'm wrong) is that they only accept past tense in this case to contrast with the second clause. I interpret it as: I understood this example (just a second ago), but I (still) don't understand the subject exactly.
The ending on "örneği" is actually just -i. It is the accusative case ending, which is used because it is the definite direct object of "anladım". This is another form of the same case ending on "konuyu" -(y)u.
So we use accusative case, but then "örneki" becomes "örneği" because of consonant mutation. When we add a suffix or case ending that leaves "k" between two vowels, it will convert into a soft g--> "ğ".
If you'd like to read more, both of these concepts are from the same Tips and Notes. I hope that helps :-)