JQuery is a javascript library providing a browser API in the functional style. In particular it supplies a CSS style selector language which makes the code for manipulating DOM objects simple and terse.

Simon Willison does a great job of introducing the library and explaining why it's so cool. For a taster, here's jquery line which loads html into a div with id 'intro'. $('div#intro').load('/some/fragment.html');

In particular I found that using CSS selectors to locate and manipulate DOM objects coupled with jquery's terseness meant it was just as easy to attach events to browser from the javascript code than by adding 'onclick' handlers in the HTML. This nicely seperates the HTML from the javascript and lets you think about how the page will behave on devices without AJAX and javascript capability.