• before_save {self.email = email.downcase}

the self.email indicates the email attribute of the current object; the email of email.downcase means to call an email method ( ActiveRecord is automatically generated for you); the meaning of this line of code is: before a User instance object is saved ( before_save ), email is converted to lowercase;
your question is converted to lowercase.
answer: self is not used in most cases, and this is the only case where you need to display the use of self .

• validates: email,. change to validates self.email,. after

validates is a class macro ( class macro ). The self in the class macro represents the current class object itself ( User ). The current class User object (class object itself) does not have a email method (the current class User has an instance method email , which is generated for you by ActiveRecord ). The
code means that before a User instance object save or update , you need to verify the email attribute; if you change it to validates self.email,. , it means to verify the email method of the User class object itself. Since the User class object itself does not have a email method, the NoMethodError