They're not saying 3NF enables you to remove foreign keys. They are talking about removing foreign key constraints from your RDBMS of choice.
Something like SQL Server can enforce foreign key constraints if you explicitly tell it your relationships between tables. The downside is that having this referential integrity costs you performance as the database has to check your relations when inserting/updating/deleting rows. E.g. checking that a foreign key is pointing at a valid primary key, checking that you aren't leaving invalid foreign keys when deleting a primary key, etc. This is to prevent you inserting bad data into the database.
You can delete these constraints and still have the exact same behavior so long as your code is correct. It just means that the database isn't going to stop you writing bad data.
Something like SQL Server can enforce foreign key constraints if you explicitly tell it your relationships between tables. The downside is that having this referential integrity costs you performance as the database has to check your relations when inserting/updating/deleting rows. E.g. checking that a foreign key is pointing at a valid primary key, checking that you aren't leaving invalid foreign keys when deleting a primary key, etc. This is to prevent you inserting bad data into the database.
You can delete these constraints and still have the exact same behavior so long as your code is correct. It just means that the database isn't going to stop you writing bad data.