A framework is a dynamic (loaded only when used) shared library along with its associated resource information. This information is packaged as a bundle. This is analogous to the shared libraries, which are placed in the Extensions folder in Mac OS 9.
Shared libraries contain code that can be shared by multiple applications. For instance, if a manufacturer produces a suite of productivity software, odds are there is going to be a great deal of similarity within their code. Therefore, from a development and deployment perspective, it makes sense to allow the applications to share common code.
Umbrella Frameworks
Umbrella frameworks are generally system software-level functions. This concept refers to a framework which itself contains two or more subframeworks. Generally this shouldn't come up in support.
Additional information
Frameworks are covered in depth at the Apple Developer Connection at:
http://developer.apple.com/techpubs/macosx/Essentials/SystemOverview/Frameworks/Frameworks.html