Mediation is a process whereby two or more parties to a dispute ask a neutral party (the mediator) to assist them in bridging the gap to a settlement or some other resolution of the dispute.
Mediation is contrasted with arbitration, where the parties select an arbitrator (neutral party) to DECIDE who should prevail in the dispute. Arbitration is generally binding on the parties. Mediation is not, and the mediator has no authority over the participants.
Often people confuse mediation and arbitration, but they are completely distinct. Typically a contract between two parties will call first for the parties to mediate, and if they cannot settle, they will proceed to arbitration.
Courts often also order parties before them to pursue mediation as part of the litigation process.
Often the best chance to resolve a dispute at mediation is when the parties take the time to engage a mediator who is familiar with the subject matter underlying the dispute. Mediators do not always need to be lawyers, although most are.
Make the confusion between arbitration and mediation all the more difficult, the American Arbitration Association is the largest source of mediators for disputes.