A CMS can greatly simplify maintaining a website, primarily by abstracting away the technical underpinnings of the web. This is fantastic for the non-tech-savvy people who have to maintain a website and the login/navigate/edit experience has become fairly ubiquitous on the web. Since this has become familiar, it's much easier to teach than muddling with FTP and remote filesystems as well.
Extend nearly any core class in SilverStripe using the Extension class: add a special route handler to a module controller; add an email obfuscation output to string-based DBFields; add a watermarking output method to the core Image class. The possibilities are endless.
My rundown of CMS's I've used (Drupal, Joomla, WordPress, and ExpressionEngine) and why my path has led me to SilverStripe. Extensibility baked in from the ground up, consistent object oriented design patterns, thoughtful MVC and ORM implementations, and excellent separation of concerns for designer, developer, and maintainer just to name a few.