As a verb:
* The mediator helped the two parties reach a settlement.
* The United Nations is trying to mediate a peace agreement between the warring factions.
* She mediated her anger by taking a deep breath and counting to ten.
As an adjective:
* The mediator played a key role in the successful negotiation.
* He was a highly respected mediator with years of experience.
* Mediation is often a more effective method of conflict resolution than litigation.
In a figurative sense:
* The large oak tree in the yard mediated the intense summer sun.
* The curtains mediate the light coming into the room.
* The music mediated the emotions of the audience.
The meaning of "mediate" in these examples varies slightly, but it always refers to the act of acting as an intermediary or being in the middle.