Chat rooms allow many computer users to engage in typed "conversation" on a given topic. You might start out with something akin to typing "hello" and then the different people already in the chat room take turns in typing "hi" back to you (but only if they want to) so that you find out who is in the room already. "Lurkers" are the people in the room who don't talk to anyone but just listen to everyone else. (See also the Chatter's Jargon Dictionary!)
Two people can also decide to have a private chat conversation. In addition, celebrities are often scheduled to "chat" at announced times. In this case, an ordinary chat room would not be large enough for the expected crowd. So a "chat auditorium" is used.
The appeal is, of course, the quick response time. Instead of posting a message and just hoping that someone will, sometime, get back to you, chat provides immediate feedback. You can "chat" with a specific person or persons about the chat room topic. Some chat rooms also have MUD (Multi-User Dungeon/Dimension) or MOO (Multiple Object-Oriented) capability which means that when you are in the chat room you can click on an "object" in the room and see a written description, such as what the person purports to physically look like (blond, blue-eyed, etc.).
Remember, on the Internet anonymity rules. This is even more critical with realtime chats where you have to be able to think fast on your feet. For a good discussion of this, see my child safety on the Internet page.
Where can you find chat rooms? Lots of places all over the Web. The search engines Yahoo! and Excite, for example, both offer chat. Or try the Chat portal Yack!