TiddlyWiki is a wiki contained in one page. You can download an empty TiddlyWiki and put it anywhere you want — on a USB stick for example. It doesn’t need any database. It’s only one HTML page with lots of JavaScript and CSS. You simply add and edit tiddlers (that’s what the parts of a TiddlyWiki are called). You can even change the layout and the colors of the wiki by editing specialized tiddlers. Once you press the save button, TiddlyWiki writes itself back into the file from which it was loaded.

TiddlyWiki makes use of AJAX. So there are no flickering reloads. It all looks nice and works smooth. You can also install plugins to extend TiddlyWiki.

TiddlyWiki is a useful application when you just need some scrapbook and don’t want to use a server side wiki. From a technical viewpoint the fact that it writes and changes itself is also quite interesting.

I always thought that AJAX is for client-server communication. So what for uses the standalone wiki AJAX?

With AJAX you don't have the normal reload flickering on each change. When you change into edit mode for a tiddler, the editor replaces the static text in place. When you close the editor it is again replaced with the updated text.

It is probably not the whole AJAX. Since it's all local in one file, you won't need any asynchronous calls to a server, but it looks like AJAX and when you tell people that an application uses AJAX they normally think "It uses JavaScript and works smooth". If you dive into the code of the wiki, you'll probably find that it's only JAX (JavaScrip and XML).