You can use a BasePage for many things you want centralized in your site. For example, as shown in the same chapter, you can use it to apply the theme based on the user's preference. You coud also use it to determine the selected menu item when you have a custom menu. For this, add a property such as SelecteedMenuItem. Pages in your site can then set this property to something like "Home", "About" or whatever, and the BasePage could then highlight the correct item, for example by setting a CSS class.
You could also use it for security where the base page looks at the current user and does something based on that information (such as displaying or hiding screen elemenets or changing their behavior).
This Google search:
brings up lots of useful example, including: