The use of XmlHTTPRequest without refreshing the browser is one of the more common ways of differentiating an Ajax application from a more traditional approach. But while rest of the world was learning Ajax, some smart developers have figured out to do the next step and created something called "Reverse AJAX", or as I call it "RAJAX".
Traditional client-server applications (not over the web) which used standard TCP/IP and UDP protocols didn't have to worry about Firewalls, NATs and PATs. Such client-server applications had the ability to intiate connections either way (from client to server, or from server to client). HTTP Protocol, which was built over TCP/IP was designed for specifically for web browsing where its always the clients asking for information and servers replying.
By moving traditional client-server applications to Web applications, the users did solve a lot of Firewall/NAT/PAT issues, but gave up a lot on usability and speed. AJAX to some extent solves the problem by reducing the amount of communication happening between the client ant the server, but it still doesn't openly allow something which servers could do in the old client-server model. Initiate a connection back to the client.
RAJAX is a framework where multiple AJAX calls between the client and server could bridge this gap and give both the server and client the ability to ask and answer to requests. An excellent example of an RAJAX application is webified chat client. Google Talk for example doesn't just open a connection when the user types in a message... it also keeps a connection open to the server to send messages to the user in case one of his/her contacts wants to initiate a chat. Another example provided by one of the reference links below is that of allowing multiple AJAX-based-document-sharers modifying the same document.
So, in short, the client always keeps an active HTTP request to the Server and allows the server to respond to that request only if there is a message from server to client which client didn't ask for.