The databases would be logically related, but not actually related in the way you think of tables being related (foreign keys).
One way of doing this is to put some tables from your schema into one database and other tables into another database. For instance, you might put your read-heavy data into one database optimized for reading, and your write-heavy data in another database optimized for writing. Those tables might still be logically related, but you wouldn't be able to use foreign keys since they are in different databases
Another way of doing this would be to have a single table split across multiple databases. For instance if you have a large site with an international presence and several data centers around the world, you might have a users
table that is partitioned across those databases with users from a given country residing in the users
table on the database closest to them geographically.