For what is worth, it separates the implementation from the interface. This is usually not very important in small size projects. But, in large projects and libraries, it can be used to reduce the build times significantly.
Consider that the implementation of Cat may include many headers, may involve template meta-programming which takes time to compile on its own. Why should a user, who just wants to use the Cat have to include all that? Hence, all the necessary files are hidden using the pimpl idiom (hence the forward declaration of CatImpl), and using the interface does not force the user to include them.
I'm developing a library for nonlinear optimization (read "lots of nasty math"), which is implemented in templates, so most of the code is in headers. It takes about five minutes to compile (on a decent multi-core CPU), and just parsing the headers in an otherwise empty .cpp takes about a minute. So anyone using the library has to wait a couple of minutes every time they compile their code, which makes the development quite tedious. However, by hiding the implementation and the headers, one just includes a simple interface file, which compiles instantly.
It does not necessarily have anything to do with protecting the implementation from being copied by other companies - which wouldn't probably happen anyway, unless the inner workings of your algorithm can be guessed from the definitions of the member variables (if so, it is probably not very complicated and not worth protecting in the first place).
