Mediators who mediate family law cases have an additional 24 hours of training in family dynamics, family law and childhood development as well.
Mediators may be attorneys or retired judges, but not necessarily. Many psychologists and social workers do quite well as mediators, because their prior training means that the mediation process is quite natural to them. Mediators come from a variety of backgrounds.
Mediators who mediate for neighborhood disputes or within certain companies, groups or organizations (non-court related), may or may not have the same training as detailed above.
If a court has ordered you to mediation, you can expect for your mediator to be a well-trained professional who believes in the process and has had the necessary training to deal with a variety of issues.