A unique role is a role that is limited to 1 player per game. For most of them, there can never be two in one game; the Godfather and Mafioso can be inherited, but even for those, only one of each can be alive at once. Currently, there are seven unique roles.
Most unique roles have abilities which would cause gameplay issues if there was more than one player with the same role. For instance, a Jailor jailing another Jailor would cause nonsensical results. Other unique roles have too powerful abilities and would upset game balance if there was more than one. The Veteran and Werewolf have these kind of abilities. Lastly, some unique roles only make practical sense if they are unique. The Mayor and the Godfather are prime examples. Because of these examples, Amnesiacs cannot become any of the unique roles. This is because if an Amnesiac becomes a unique role while a Retributionist resurrected the same person, there would be two players with unique roles and therefore would upset the whole point of a unique role.