VFP Help defines a persistent relationship as "Relationships between tables that last longer than just at run time. Tables must be in a database to have a persistent relationship.".

A database is a container for tables. Inside that container, relationships can be set once between the tables in the database, and need not be set again - they are "persistent". Relationships set between tables that are not in a database, or between tables in two different databases, do not "persist" - the relationship disappears when one of the tables is closed, and must be reset using the SET RELATION TO command.