The easiest way to understand the callback example is to invoke the Hello User web script directly and interrogate the response.
Type the following in the command line:
curl -uadmin:admin "http://localhost:8080/alfresco/s/hellouser.json?alf_callback=showGreeting"
This mimics the web script invocation made in the callback.html file.
The response is:
showGreeting({greeting: "hello", user: "admin"})
This is simply the vanilla Hello User web script response passed as an argument to the function named showGreeting as defined by the alf_callback query parameter. The full response is treated as JavaScript by the web browser, which executes it.