These days software applications are complex in their functions. It is an arduous task to build an application on top of all own handwritten code, and it is not advisable.
It is in practice to build applications by combining owned code with shared code to match up with the fast pace of world demand of software.
Code is distributed/shared as Libraries(tangible unit).
Frameworks and Toolkits are aspects of Libraries.
A framework enforces you to write code in a set of code chunks (framework elements) and calls your engineered code-chunks to do its business. You are never in-charge of calling these code chunks.
Typically, you annotate or mark your code elements (classes, objects, method) with framework elements. Marking process may vary language to language.
Framework can be categorised into
In simple words, a Toolkit is just a set of functions or code elements. Your application code calls these functions or elements. You are in full control of calling these functions.
jQuery is a web library which provides DOM manipulation utilities.