Parties mediate cases because mediation is generally cheaper and faster than going to the courthouse for a trial. Some cases are mediated before a lawsuit is filed and others after the suit is filed. If a dispute is settled before a case goes to trial, the parties do not have the expense - in time, stress, and economic commitment - which is required in litigation. And the parties can control how the dispute is resolved. Cases which are heard before a judge or jury often result in a judgment in which the parties have lost control of some of all of the issues in a dispute.
Mediation is fair; the parties remain in control; and mediation is safe.
Mediation is fair because the mediator is fair. The mediator is impartial - and is not on any one's side. The parties are in control in that they can discuss at a mediation anything they want to discuss - not just legal issues which judges can control. And the parties are in control because no one is required to do anything at a mediation. If a party does not like the proposal of another party, no one has to accept the proposal. The case can go on to resolution in court or some sort of settlement at another time.
Mediation is safe because it is confidential. The settlement discussions at a mediation are considered confidential, and no one can tell a judge what was discussed at a mediation - or ask anyone else to disclose the content of the discussions. And when a mediator is talking with one party (and the party's lawyer, too), the mediator cannot tell the other party what has been said unless given direction or permission to do so.