This is a really a great micro-framework for writing small applications with only a few pages or like middleware APIs.
The main benefits are that it is based on the Symfony framework which is a full of quality framework and decoupled in multiple components that you can re-use independently on your applications.
There is also a lot of Silex built-in providers that allows to use these components into Silex such as Twig, Asset management, Doctrine, Form, Translation, and much more...
Finally, in the case of a micro-application that only do one single job, you can write your Silex application in only one PHP file.
It's a micro-framework so you have to define your project structure yourself, there is no really best practice to organize your things, it's up to you.
You cannot use Symfony bundles into Silex as it is not bundled with Symfony Config component and mechanism that could allows that.
Writing high-performances and small applications and also micro-service applications that could be APIs for example.
Problem solved for me are really based on performances because you don't have to load a lot of libraries as it is done on a lot of frameworks. Here, you only load providers you need into your application.