Mediation is a process where both parties work together to decide on a resolution regarding their case/issue.
Arbitration is a process where a third party hears both sides, and makes a decision in favor of one side or the other. It's much like the court process, but with fewer rules, and it takes less time.
Lawyers can be used in mediation, and should be used in arbitration. In mediation, lawyers should only serve to make sure that you're not agreeing any of your rights away. Other than that, attorneys in mediation should allow you as a party to work with the other party directly to come to a mutually agreed upon decision.
Mediators should always be impartial and fair. We are there to help you have the discussions you need to have; to keep track of what you're agreeing upon; and to write up your agreement.
Mediators are cheaper than using attorneys, going to court, etc.
The original poster posted a while ago, but hopefully this helps future readers.