In arbitration, you and your spouse agree that you'll hire a private judge, called an arbitrator, to make the same decisions that a judge could make, and that you will honor the arbitrator's decisions as if a judge had made them. Arbitration has some of the same advantages as mediation does, including speed, efficiency, privacy, cost-effectiveness, and informality.
Arbitration has been used for many years in other kinds of lawsuits, and it's starting to gain favor among divorce lawyers as a good alternative to a court trial. The arbitrator is usually a lawyer or a retired judge, who you pay hourly. Your lawyer and your spouse's lawyer know lots of arbitrators and will probably be able to agree on someone who'd be appropriate for your case.
Just as in a trial, each side prepares arguments and evidence and presents them to the arbitrator, and then the arbitrator makes decisions. However, the presentation of evidence is usually less formal than in a courtroom. You're likely to be able to schedule a hearing with an arbitrator much more quickly than you would get a case to trial, so speed is a major advantage. It's also private, unlike a trial, which is open to the public. (Your court records will still be public if you use arbitration, though.)
Cost is another upside to arbitration; although it's still expensive, it won't cost as much as a trial. That's because it shouldn't take quite as long for your lawyer to prepare for the hearing, and the arbitration itself may be shorter because the arbitrator won't be as strict about evidence as a judge would be.
An arbitrator's decision generally is binding, which means if you don't like it, you can't ask for a do-over and go to court for a second chance. You also can't appeal the decision to a higher court, so you are stuck with whatever the arbitrator decides. Because of the inherent unpredictability of divorce cases, some people don't like that idea—though some might appreciate the certainty that arbitration offers.
Arbitration isn't available everywhere. A few states don't allow arbitration in divorce cases. Check with your lawyer, if you have one, or with your local court clerk.