If your two best friends are fighting over the last piece of gum in the pack, you might arbitrate by telling them to split the last piece. Arbitrate is when a neutral third party helps end a conflict.
Arbitrate derives from the Latin arbiter "judge." (An arbiter of taste is a good judge of taste.) When you arbitrate, you are doing what a judge does in a court of law. In the US, to avoid litigation, many choose non-binding arbitration—where a neutral third party suggests a settlement.