Diplomatic Agendas are a major driving force in your relationship with other leaders. They drive the desires and behavior of those leaders. You can use Agendas to know how to get on a leader's good side, or what to do to avoid making them angry.
Leaders have a Historic Agenda and a Hidden Agenda. The Historic Agenda is based on that leader's real-world historical personality and achievements. The Hidden Agenda is assigned at beginning of every game, and could be a wide variety of things—maybe they like other civilizations with lots of culture or gold, or maybe they dislike warmongers. Revealing the Hidden Agenda is important to knowing what pleases and displeases a leader. Increase your Diplomatic Visibility with each civilization to find out what their leaders' Hidden Agendas are.