I would define a framework as any software or collection of software which acts to support the development of other applications.
In my case, in particular, the framework I have is both tool and organization dependent. Then, I suppose that at the most basic level, some items could be used for projects outside of the company, but there are libraries in the framework which are very specific to projects. The base framework, however, is portable across projects. It is very much dependent on the tool we use, though.
I'm a lead developer of a generic open source test automation framework called Robot Framework (not related to Rational Robot or java.awt.Robot for that matter). It has a pretty standard framework architecture with a common core that can be be extended with test libraries. If you want to study and/or use it take a look at http://robotframework.org