I see that every package is part of some component, and that PiSi has commands to list components. But what are they for, and where are they used? Could someone give an overview of this?
It's for package-manager, you see the components on left side, right? It's done with component.xml files in each directory

If we set "<VisibleTo>user</VisibleTo>" tag in component.xml, this component will be shown in package-manager. That's why a lot of component is shown up when you add Contrib repository (e.g, Xfce Desktop, Compiz Fusion etc..)
Also, this component hierarchy makes svn repository tree understandable and useful.
http://svn.pardus.org.tr/pardus/devel/desktop/kde/component.xmlhttp://svn.pardus.org.tr/pardus/devel/applications/multimedia/component.xmland so on.