Mediation is a process where both parties to a dispute (and their attorneys if they have them) sit down with a neutral third party who assists them in reaching an agreement or settlement. Mediators are usually trained in a variety of techniques. The mediator is only there to facilitate an agreement, and has no power to render any sort of judgment in the dispute, though they may give their opinions as to what would be the likely outcome in the court system.
Many judges order parties to a case to attempt mediation before the case is set for trial in hopes that a settlement will be reached. Some jurisdictions have made this a required step in certain kinds of litigation.