"Thin client" is a term that refers to a compter, terminal, software program or device which handles user interaction with applications, but does as little processing as possible in and of itself.
The opposite, a "thick client" handles not only communication to the server and interaction with the user, but processing, rendering images or text, and other computationally non-trivial tasks. Examples of thick clients are web browsers, e-mail programs, and the like.
Thin clients are often nothing more than remote access to another computer. The programs run on the application server, but rely on the thin client for user interaction. Examples of software Thin clients (that run within a desktop computer's host OS to provide connectivity to an application server are Citrix, VNC, PC Anywhere, Microsoft Remote Desktop and Remote X11. There are also hardware thin clients such as WYSE WinTerms, SunRay terminals, and even those old orange or green-screen VT text-only terminals you used to see in businesses and libraries in the 80's. Usually, the monitor physically attached to the application server doesn't show any sign of the applications being used via thin clients. Exceptions to this rule are RDP Console connections, VNC Server and PC Anywhere on Windows, or X0 VNC on Unix platforms, all of which take control of the "console".
Windows 2000, 2003 and XP can readily accept RDP connections. Server editions of these OSs allow more than one person to login at once. An RDP client ships standard with most MS Operating systems, including PocketPC, Windows CE and Windows Mobile on newer PDAs. You can also get RDP Clients for Windows 95/98/ME, UNIX/Linux, and MacOS. Certain hardware thin-clients, such as WinTerms can also connect to RDP hosts.
You can easily get VNC server (an open-source cross-platform remote control suite) installed on Windows, Mac or UNIX. Client software is available for almost every modern operating system, including certain PDAs.
X11 Servers are also available for most platforms, allowing you to run graphical UNIX apps on a server while "beaming" the windows the applocation creates across the network onto your X11 Server display. The term "X11 Server" is somewhat confusing, in that one typically associates "server" to be the host. In a sense, the X11 protocol runs as a "service" on the X11 client system, allowing applications on UNIX servers to draw their windows onto the thin client's display.
The beauty of thin client software is that you can breathe new life into an old 486 or Pentium simply by installing Windows 95/98, or some BSD or Linux variant. Simply install the thin client software packages of your choice. With X11 or VNC Server on a UNIX host, or remote desktop on a Windows server, you can theoretically have many users logged in simultaneously on their own session, sharing one really powerful computer and relying on the old, seemingly useless computers to provide the interface.
Where there's no way that the latest versions of Windows server 2003, Office XP, Mozilla firefox and thunderbird would run on a pentium 60 with 32MB of RAM, you can just set up Remote Desktop, and turn this old PC into a second monitor, keyboard, and mouse to an existing machine. Since most thin client programs work over TCP/IP, you can put this terminal in your study, in the kitchen, or even in the kids' play area. With a properly configured network connection at home, you could even use thin client software to remotely control your home computer from the office, coffee shop, while vacationing in Barcelona, or anywhere you can get adequate Internet access. Note: employers are starting to crack down on thin client and VPN use from work because of its potential as a malware vector or productivity threat.
Due to the climate of the Internet today, I'm not an advocate of putting Internet-facing computers in kids' bedrooms or other places where they can remain un-supervised for long periods of time, but that choice is yours to make, and there are many other places in the modern home where a thin-client system could come in handy.