Household, which is a grouping of entities, for example you want to group entities belonging to the same family. Household is not one of the out of the box data types this is supported by the data migration import process. The data migration import process can be extended to support household, for the steps on extending the import process, refer to the data migration import developer’s guide.
Hierarchy is the organizational structure that an entity is a part of. The DMContact.externalParentId is used to identity the immediate parent of a contact within the hierarchy.