A story about an orange.
An orange tree grows on the side of your yard. An orange drops from your tree onto you neighbor’s lawn, and he wants to keep it. You believe the orange belongs to you. So you tell it to a judge. After reading about your case, the judge says that you should cut the orange down the middle, and each of you should take half.
That’s a traditional, understandable decision. But suppose you asked a mediator whose orange it was. The mediator would ask both of you many questions about your wants and needs for this particular circle of citrus. Turns out, you want the pulp to make juice, and your neighbor wants the rind to bake a cake.
Aha! You each still receive half, but you get the entire part that interests you in the first place. That’s the beauty and the benefit of mediation.