Serialization uses certain default behaviors to store and later recreate the object. You may specify in what order or how to handle references and complex data structures, but eventually it comes down to using the default behavior for each primitive data field.
Externalization is used in the rare cases that you really want to store and rebuild your object in a completely different way and without using the default serialization mechanisms for data fields. For example, imagine that you had your own unique encoding and compression scheme.