Resolving a fetter is a process of saying farewell, enacted through roleplaying. During the process, the wraith comes to terms with his mortality and the relationship it has with the fetter. Doing so progressively reduces the fetter's rating, until it can be formally resolved and reduced to zero.
Apart from the benefits for Transcendence, resolving one's fetters allows a wraith to travel more freely. A Wraith who resolves his fetters (A Gaunt) can travel anywhere in the underworld freely, a wraith with unresolved fetters feels a tug back to them in the Tempest or Stygia.
Passions can be resolved using the same system, although resolving them does not provide a benefit outside of transcendence.