jQuery is a framework for javascript language, which allows developers to create great effects, outstanding features faster

Formal description:

jQuery - JavaScript library, which focuses on the interaction of JavaScript and HTML. jQuery makes it easy to select any DOM element and manipulate the element's attributes or content. jQuery also provides a convenient API for working with AJAX.

In other words:

jQuery - set of ready-made functions and methods of JavaScript, which greatly simplifies the interaction with design page elements, significantly reducing the overall development time.

What is it used for?

jQuery is utilized for crafting custom web page elements, such as, creating visual effects, drop down navigation menus, and form validation. These elements combine to make your website much more convenient and entertaining for the end user.