The wife calls me after a long mediation session and says, "Do you know what you are? You are a witness."
For her, that was my important role. As David says, your clients want your approval, and any acknowledgement you can offer is greatly appreciated as long as you appear impartial.
I come to believe in many quarrels there is no truth. Each person has her or his own reality, often quite different. If both can hear from the mediator recognition that they are trying to do the right thing, that must be very comforting: a step opening towards a more constructive direction.