"IDENTIFIED BY 'password'" in MySQL

I often see in many MySQL tutorials that people use command IDENTIFIED BY 'password' both during user creation and granting him privileges.

For example:

CREATE USER 'username'@'localhost' IDENTIFIED BY 'password';
GRANT ALL PRIVILEGES ON database.* TO 'username'@'localhost' IDENTIFIED BY 'password';

I tried using GRANT without IDENTIFIED BY and it works.
Can somebody explain me why it is used twice? Could there be other password for specific privileges?