A neutral moderator plays a role if the parties involved need an unbiased person that can lead the conversation. It especially useful in conversations where tensions have already risen, but have not been preceived as a "conflict" yet; a large or mixed group of people; or when those involved do not want any discussion about the chairman.
Online Neutral Moderator
Being a conversation leader in an online conversation is a lot more difficult. In a situation where every member is physically present, it is usually possible to assess what those present think of a situation. You recognze the non-verbal behavior of someone that wants to contribute easily, for example when you see them pop up in the corner of your eye, you hear small mutters from them, some shuffling in their chair, or you see them completely give up . It is often difficult to spot such signals in an online meeting. In addition, it is harder to interrupt in online meetings, since most tools only allow the sound of one person at a time. The result is that an online conversation leader is often focused on the content and 'forgets' to lead to conversation.
A neutral moderator can offer a solution. I am, as a neutral moderator, used to taking charge in an online meeting. I focus mostly on the process, and thus giving balanced space to all participants.