IMO: Your business logic should remain on the server. The client should handle the user interaction like it always has in the real world. This ensures a level of security in your application. Ajax sends the data to the server to be processed and the client side code should take this data and make it available to the user.
The basic concept of Ajax is we are not pushing around the full weight of the page. We do not have to render the entire document time and time again to just figure out if one textbox has the right content in it. This means less data transfer back and forth per request, we do not loose the page's state and we can allow processing in the background while the person is still filling out a form. You see the processing taking place with google maps.
Look at this
thread here, you will see some good uses of this technology. With Balaji example, you would not be able to do this effectivily without the XMLHttpRequest Object. You could use iframes, but that has problems. We talk about the problems with the traditional methods in the book.
Hopefully I answered your question..
Eric
