Additional insights into intermediary roles are offered by Beyond Intractability project participants.
Intermediaries (or "third parties") are people, organizations, or nations who enter a conflict to try to help the parties de-escalate or resolve it. They generally do not take sides (although they can, on occasion, be partisan to start with -- see the essay on "insider-partials").  Intermediaries can be formal or "informal."
Formal intermediaries are people who are professional conflict resolvers and who are hired specifically to do that job. They may be professional mediators, arbitrators, facilitators, or judges, who work privately or with a government agency (even representing the government itself as with official diplomats). At the international level, these people are referred to as "Track I" diplomats, as distinguished from "Track II" diplomats, described below.
Informal intermediaries are people who find themselves in an intermediary role, but it is not something they usually do as a profession. Parents breaking up a fight between children, friends intervening to help another couple save their marriage, people trying to solve a community problem by having some people over to their house for a talk are "informal intermediaries." So too are private citizens or non-governmental organizations who try to build bridges between hostile nations.
For example, the organization Seeds of Peace brings Palestinian and Israeli teenagers together at a camp in Maine (U.S.A.) to try to build understanding and friendships between them. Normally, informal intermediaries are non-governmental actors, such as religious institutions, academics, former government officials, non-governmental organizations, humanitarian organizations, think tanks, who try to act as a go-between to try to de-escalate or even resolve an intractable conflict. At the international level, this is referred to as "Track II" diplomacy.
Formal or informal, the most visible and recognized intermediary roles are mediators and arbitrators. But there are other roles as well. In his book "The Third Side," Bill Ury identifies 10 such roles:
- Provider (of needed resources)
- Teacher (to give new ideas for how to resolve the conflict, or at least for new ways to approach it
- Bridge-builder, who (like Seeds of Peace) brings people together where they can get to know each other better
- Mediators (who help parties work out their problems themselves)
- Arbitrators (who listen to both sides and then make a decision about what should happen)
- Equalizers (who empower the lower power group(s) so that they can then negotiate more effectively with the other side)
- Healers who help parties to apologize, forgive, and become reconciled
- Witnesses who observe what is going on and call attention to injustice or human rights violations
- Referees who try to keep both sides "fighting fairly" and
- Peacekeepers who try to keep the parties apart so they don't fight (at least physically) at all 
Since intractable conflicts tend to be intractable because they are very complex, with many parties, many deep-rooted issues, and no apparent, "way out," all of these types of intermediaries have a role to play, perhaps not all at once, but over the course of the conflict. Rather than detailing these roles here, they are discussed in the essays on each party and also on each process.