Diplomacy

How does diplomacy work? I am playing the Barbarossa campaign and was being attacked from all directions. I went to the diplomacy screen and changed Henry the lion to an ally, paid some tribute and sure enough he stopped attacking

Why did this work, what is the logic behind it? Is there some specific sum you need to pay in order to get the other part to change to friendly too? I doubt you can convert enemies just by setting the dials in the diplomacy page