I've read the Wikipedia page, but I don't really have a "big picture" understanding.
Could anyone give me an overview and potential applications?
Frameworks are like incomplete / partial applications. They solve most of trivial tasks for you and allow you to focus on business logic directly. You stuff your business logic into it to make it complete.
For example, web frameworks like Spring or Struts, solve most of the request / response related trivial tasks like getting parameters from a request and populating model beans from it, rendering responses depend on model values, security, request dispatching etc. So you can utilize these structures to quickly develop applications.