What is ON DELETE part of the foreign key constraint?
If you set it to CASCADE, then your delete from the parent table will cascade to child tables (to put it simpler, when you delete record in table A, then PostgreSQL will delete any rows in tables B and C that are referencing original row (or column) in table A).
If you used defaults when you created your FOREIGN KEY constraint, the default is to restrict ANY deletion in table A if it is being referenced in table B or C.