There is no exact listing anywhere of what level gives you what, it's more of a general amount of how much gossip you will get (and frankly it becomes an annoying amount late game).
EDIT (Info moved from comments):
Certain information is only available at certain levels. In the early
couple stages you only get access to things like war declaration,
denouncements and their first hidden agenda, and a vague idea of what
they think of you.
By the higher tiers of visibility you begin to see the second agenda,
clearing land for wonders and war preparation - basically the higher
you get, the frequency increases and the more strategically value the
Visibility is the amount of information you are currently able to obtain about the other civilization.
When you click on the Access Level button, you will see in the bottom part of the UI, a breakdown of all active factors currently contributing to Visibility. You will also see what kind of info you share on this level, and what you may expect to see in the next level of visibility.
- Arguably the most important things you learn through gossip and visibility are: when a nation clears land for a wonder, when they are preparing for a war, and when they denounce other nations. Each of those provide valuable strategic information about other nations.
Visibility is provided by the following factors, which are cumulative:
- Sending a Trade Delegation or Establishing an Embassy. (These two are not cumulative)
- Having a Trade Route with them.
- Being Allies.
- Having a Spy create a Listening Post in one of their cities. This action does not stack with being Allies.
- Research Printing technology. This automatically gives you one level of Visibility with all nations.
The gossip part of the game doesn't have a lot of recorded detail to explain it, but you can get the gist of it through the diplomacy tab of the wiki.