Advantage of using a class library is that types and implementation is defined and updated in a single place and can be consumed by multiple applications. Sometimes it is required that multiple applications use a commonly defined type.
Disadvantage of a class library is that all consumers is affect if library is changed and may have to update client code as well, unless they can keep using an older version of it.
An interface is a type (without implementation), so the above applies to that as well. Specifically an interface can allow different applications to exchange and interact with different types by implementing this common interface type.