Multitouch is a technology that can use two or more fingers as input... as a control, as a trigger to do something. You may have used a touch screen before, for example, my local convenience store uses touchscreen ordering systems in their deli. But I'm not able to use two fingers, so their system is single-touch and not multi-touch.
Multitouch can be used on top of current technology, such as within an operating system like Windows 7, in which is is an enhancement to a standard GUI (graphic user interface), in multi-touch circles referred to as WIMP (standing for window, icon, menu, pointing device).
When the control of the computer or device is oriented completely around the multitouch manipulation, the term NUI (natural user interface) is often used. Apple's iPhone is one of the most popular multi-touch devices currently on the market.
The branch of study that deals with multitouch is called HCI (human computer interaction).