The Ajax Requests area represent 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 times for each request. The <a4j:queue/> (defined as global for the form where controls placed) handles all the requests and fires next one only after the responce from previous returned.

The demo JavaScript on the client includes a function that subscribes 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 they were fired.

Queue demo