AJAX is a technique that does not really represent a full solution (in comparison to the other strategies presented here). But it is a novel technique that will probably give rise to a host of other strategies, hence its inclusion here, and in such a prominent top-level location in the ControllerTaxonomy.
AJAX refers to the use of JavaScript together with the ability of modern browsers to change an HTML document while it is already being displayed in the browser. (See http://java.sun.com/developer/technicalArticles/J2EE/AJAX.)
Using plain HTML (without JavaScript), events are only sent to the web server when a form is submitted via a button click, or when a link is followed. JavaScript can attach code to other UI elements on a form.
AJAX refers to the technique of using JavaScript to intercept such UI events on the browser, and then making a request to a web server without disturbing the original document being displayed (or the current state of the browser). Upon receipt of the response of this background request, JavaScript is again used to change parts of the contents of the original document---all while it is being displayed.
Such a background request is a request for more information from the web server, not for a complete rendered page (since the page is already rendered, and just needs to be modified). For this purpose, such requests usually request XML documents, which are nothing more than containers for generic information which the AJAX code in the browser is able to make use of. This information can be used to populate a selection box, for example, depending on the current state of another radio button.
A framework built on AJAX has the advantage that part of the executing UI program is on the client. (The bits of program can also be sent to the client as and when they are needed instead of having to send an entire progam there in one chunk.) Session state information can also be kept here (where it's needed) instead of encumbering the server with it (where it hampers scalability). This difference has potentially far-reaching effects for specification techniques and is the reason why it is expected to spawn a new class of web framework.