This little tutorial explains a way how you can retrieve more parameters from Yii::app()->user by adding a component that extends CWebUser and retrieves the user information from database table named User.
These features provide endless possibilities and unbelievable flexibility, but as current documentation does not give more than a few examples, it might be difficult to fully understand their internals and requirements.
Authentication and Authorization is a good tutorial. Among other topics, it describes basic aspects of Yii's RBAC implementation. But however hard I read the tutorial, I couldn't understand how exactly the hierarchy works. I found how to define authorization hierarchy, how business rules are evaluated, how to configure authManager, but almost nothing about how I should build my hierarchy, in what sequence its nodes are checked, when the checking process stops and what would be the checking result.