What changes, or what it is obtained, in my stackoverflow account (or any other) when 200 (total) rep is reached?
You can access the privileges page from your account dropdown menu in the header:
There is also a 200 rep per day limit (from votes) you may have heard of, which is something entirely separate. That is mentioned in How does "Reputation" work?:
You can earn a maximum of +200 reputation from upvotes and suggested edits in any given day. Accepted answers and bounties are counted separately. Reputation "lost" from the reputation cap is not awarded on following days.
You can read about why that's the case in What is the reasoning behind the reputation cap?