Nothing. There is no requirement for your controllers to have before() and after() methods.
They are present in the base controller (in this case Controller_Template), where before() will make sure that $this->template contains a View object for your action method to work with, and after() will make sure that if your action method does not return a Response object, the returned value will be wrapped in one.
In general: before() can contain code that has to be executed for every action method called in your controller. A typical example is some template prepping (for example set a title or navigation, a sidebar perhaps), or access control. Similarly, an after() method is called after the action method is finished, again for some generic code.
If you don't have a use for them, don't include them. If you use them, make sure you call the parent otherwise the controller will no longer work properly.