A CComponent by itself doesn't do much. It's very much like a QObject in Qt. A CComponent can raise events, and can have delegates to events (through attachEventHandler()).
Regarding behaviours, the manual says:
The methods of the behavior can be
invoked as if they belong to the
component. Multiple behaviors can be
attached to the same component.
To attach a behavior to a component,
call attachBehavior; and to detach the
behavior from the component, call
detachBehavior.
A behavior can be temporarily enabled
or disabled by calling enableBehavior
or disableBehavior, respectively. When
disabled, the behavior methods cannot
be invoked via the component.
Starting from version 1.1.0, a
behavior's properties (either its
public member variables or its
properties defined via getters and/or
setters) can be accessed through the
component it is attached to.
Which gives you the possibility to simulate a signals and slots mechanism, or the strategy pattern (by enabling or disabling behaviours).
Most of the classes in Yii have CComponent as a base class.
As a user, you'll see the benefits they provide through the mechanisms mentioned above when you'll create your own components (under protected/components/).
You can find a good starting point for implementing components here: http://www.yiiframework.com/doc/guide/basics.component