Arbitration is useful when one side or the other (or both) prefer to have someone neutral decide the matter for them. This usually occurs if one party or both refuses to compromise on any issue.
Arbitration often works well for commercial and business disputes.
Arbitration is more formal than mediation, but less formal than court. You and the other side agree in advance on the rules for the arbitration process (for example, what kind of evidence can be introduced, will witnesses be allowed to testify, how much time will be set aside for each side to present its case, etc).
The arbitrator listens to the evidence you each present and then makes a decision. In many cases, it is agreed beforehand that whatever the arbitrator decides is final and binding. This means you cannot have the decision reviewed or changed and must live with the outcome.
Due to the high costs of trial, the associated delays and the unexpected outcomes, in most cases, settling your case through negotiation, mediation or arbitration is preferable than risking it all and going to court.