A deletion with cascades means that if the tuple that is part of a foreign key for another tuple in another table is deleted, that deletion cascades downwards and also deletes the tuple.
A deletion is done using the following SQL statement:
DELETE * FROM users WHERE username = //username//;
The deletion on cascade is implemented when the table is created (or when it's altered) like so:
FOREIGN KEY (username) REFERENCES users (username) ON DELETE CASCADE
You can see this in action [ here ] by clicking on any user profile, and deleting the user. Then, navigate to the list of posts, and you can see that all of the posts from that user are deleted.
A deletion without cascading means that even if that tuple is deleted, other tuples are not deleted.