1) The first example is a custom field type that you can add to any document library and that returns the main properties of any document by
clicking on it in a fast and user-friendly way. Thanks to the jQuery code embedded in the CAML of the custom field type, the properties are returned via an AJAX query that calls lists.asmx to get the properties. 
This example is the main topic of the video and is rebuilt from scratch.

2). The secund example will be available for download and is overviewed during the video. It's a custom SharePoint calendar where users can type locations in a textbox. All the matching events are highlighted within the calendar directly (they blink) and direct links to the events are shown above the input textbox. 

Again, same principle than for the first example (query to lists.asmx) but this time the jQuery code is isolated in a separate JS file and both the jquery javascript file and the custom one are included OnPreRender of the custom calendar control.

To watch this video, click here.

jQuery is a fast and concise JavaScript Library that simplifies HTML document traversing, event handling, animating, and Ajax interactions for rapid web development (wikipedia article). It was created by John Resig and dual licensed under the MIT License and the GNU General Public License, jQuery is free and open source software.

Marc D. Anderson developed a jQuery library names "jQuery Library for SharePoint Web Services" which abstracts SharePoint's Web Services and makes them easier to use. It also includes functions which use the various Web Service operations to provide more useful (and cool) capabilities. It works entirely client side and requires no server install.

You can download it or you can read blog posts about this project(on Marc D. Anderson's blog)