There are actually two components to TouchMouse; the iPhone app and the Logitech TouchMouse Server software. The latter comes in Mac OS X and Windows (XP, Vista, and 7) versions, and must be installed on the Mac or PC in order to "host" the virtual mouse and keyboard created by TouchMouse.
The "mouse" has three buttons for your "clicking" pleasure, and uses the majority of your iPhone screen as a touchpad. With the touch of a button, you can bring up a keyboard to type on your Mac or PC.
There are other apps that can do the same thing if you're not a fan of Logitech. Air Mouse Pro [US$1.99, iTunes Link] is probably the most powerful and popular Wi-Fi mouse in the App Store, while Rowmote Pro [US$4.99, iTunes Link] has a large and vocal fan following. If you're looking for free (and who isn't?), Logitech's TouchMouse app can give you a taste of remote control at absolutely no cost.