Relationships determine what you are or what role you play when placed in any environment. Likewise, relationships in the Private Media Channel determine the user's connection or the role that they will have in a particular community.
But, this is important, to set the Relationships you must first set the Roles. So go one step behind, manage roles and come back here to set the relationships.
Here's how you do it. Click on Community > Manage Relationships and then click on the user for whom you want to set the relationship.
Here you find the community and the corresponding roles that can be given for that user. This determines the relationship of the user with each community in particular. Oh! and don't forget to hit save when you are doing setting it up.