The User Relationships module allows users to create named relationships between each other.
Relationship types are defined by an administrator at: Administer > User Management > Relationships (for D7: admin/config/people/relationships).
Relationship types have a name, a plural name, a time-out, an auto approve designation and a directionality. The name can be anything. The time-out is the amount of time a request stays active. For example, if it's set to 30 days and a user requests a relationship with another user and that user doesn't accept or deny the request within 30 days the request will be dropped.
If auto approve is set, the system skips the request->approve/deny process and simply creates the relationship. An application of this might be the relationship type "subscriber." You don't necessarily need to approve of me subscribing to you.
An example of a two-way relationship may be "friends." If you're my friend I'm your friend. This is the default for new relationships created with User Relationships.