JQuery is a fast, small, and feature-rich JavaScript library. It makes things like HTML document traversal and manipulation, event handling, animation, and Ajax much simpler with an easy-to-use API that works across a multitude of browsers.
Beware that JQuery version 2.x does not support IE 8 and earlier versions. Instead you need to use JQuery version 1.x.
JQuery is a library of Javascript methods and properties. This has documentation for that library along with small examples.