The technique is called Comet, aka 'server push'
There are currently 2 main ways of implementing comet.
1) As Daniel mentioned, long-polling, where you can use ajax to leave a hanging request to the browser that doesn't send the response back until the server decides to (whether it be based on someone else's actions or another server event).
2) The second approach, used by Google, is streaming. This involvs using ajax to leave a hanging request, but the response is never sent back to you, ever. Instead, the server updates bits of data and you use javascript to monitor changes, and fire events based on new data being pushed in. What happens is you get one very long continuous stream of data flowing in on a document that never closes, taking new data as it comes in.
HTML5 has a specification for a simpler way to do this with Web-Sockets. In the future, this type of live web-app will become commonplace as Web-Sockets are easy to use, but it is not supported on all browsers yet.
If you want to build a Comet site for production, you'll need to use a non-blocking I/O async server like one of the following.
http://www.tornadoweb.org/ - python
http://nodejs.org/ - server side javascript
-- or google for comet servers.
You'll need to know how to program for comet type apps on the server-side, as the javascript for Comet is pretty trivial, just your normal ajax calls with a couple event handlers.