The civilization with the most 
Envoy Envoys on a city-state, and at least 3 Envoy Envoys, is considered that city-state's Suzerain. There can be at most one Suzerain; ties are not allowed. If nobody has Envoy Envoys on a city-state, there is no Suzerain. The Suzerain gets several significant benefits, which are described below.
Unique city-state bonus: This is a powerful bonus which no other city-state will provide. For example, Jerusalem acts as a second Holy City for your religion, meaning that Jerusalem will exert religious pressure on nearby cities and city-states.
Diplomatic allegiance: The city-state will automatically follow its Suzerain into war and peace, matching the diplomatic state of the Suzerain.
Resource sharing: All of the city-state's resources are automatically exported to the Suzerain, and the Suzerain may build tile improvements in their city-state's territory.
When at war, the Suzerain may also pay 
Gold to take control of the city-state's military units for 30 turns. The amount of Gold that needs to be paid is determined by the size and strength of the city-state's military.