Silex is a microframework meant to be used in small projects. It's suitable for small websites with low traffic. It is also a good way to introduce yourself into some concepts like dependency injection, without introducing too many abstraction layers. They've recently introduced the target in their website as "single-file apps", giving you a bit of the target scope for the framework.
I think it should be fairly accepted fact that Silex is not suitable for anything big. Silex will not perform badly if your project works, but it will not be the nicest to work with once you start growing, as it will not help you too much. Symfony uses concepts you'll see in Silex and is a full stack framework you can use for bigger applications with lots of bundles, plugins and a big community there to help you.
AllEdit:
Note I cannot delete the answer as it has been accepted. I haven't used PHP in allyears now, it wouldn't be my first choice forsince then, Silex has changed their approach from "microframework" to being just a frameworklibrary it seems. Whatever the case, once you get comfortablethe down-voting I believe must come from people involved with bigger frameworks there's usually no need to limit yourself by usingthe project, probably upset of having created something which didn't take off as they may have hoped.
Just read the product docs, this was a small onerequest for an opinion which was given and accepted. I don't think this question belongs to stackoverflow anyway.