Chat rooms (or, to give them their proper name, Internet Relay Chat Channels) allow groups of people to exchange live text messages. When you log into a 'room' you see a scrolling window containing messages from everyone else in the room. You can type messages too, which also appear immediately in the scrolling window.
The interchange of messages is handled by a central IRC server, and there are plenty of servers around which will host a chat channel for you free of charge. Chatting via an IRC server used to require a stand-alone IRC client application. However IRC clients are now available as Java applets, which you can call from your own web pages. When such a page is opened, it downloads the client applet from the IRC server. The applet then connects to the server, and automatically opens your channel. Your site's users can then chat from your page via the applet's display, which includes the message window, input box and, of course, those vital banner ads.
Chatrooms are a great way to bring like-minded people together. However one potential problem is that, unless your site is wildly popular, it's likely that anyone logging in won't find anyone to chat with - avoid this by scheduling chat 'events' at specified times. There are some unsavoury people out there too, so be ready to use your moderator privileges to eject unruly visitors.
There are plenty of web-based chat servers around, all offering much the same feature set, so the choice really comes down to things like the speed of applet download and how big and annoying the banner ads are. Make sure, however, that your server offers basic controls such as banning unwanted participants. The major players include www.chatplanet.com and www.parachat.com, or for a rare non-American free resource, try the Anglo-French http://uk.maxichat.com.