The Ajax Requests area represents individual Ajax requests that can be fired by clicking the green images (a4j:commandLink components). A JSF managed bean on the server causes a random sleep time (4 seconds or less) to simulate different processing time for each request. The <a4j:queue/> (defined as global for the form where controls are placed) handles all requests and fires the next one only after the response from the previous returned.

The demo JavaScript on the client includes a function that is subscribed to these queue events, so the UI is updated as queue events happen.
Just click on any sequence of green images (any number, any order) and you will see that each request is handled in the order it was fired.

Queue demo