Quartz Compositions are created using the Quartz Composer application (included when you install the Mac OS X development tools). Quartz Composer allows you to graphically program Quartz Compositions by creating and connecting nodes together. In MixEmergency they are generally used to create some sort of visual output - much like how there are some applications that allow you to program "audio visualisers". The files as such are just XML property lists. When loaded into applications, such as MixEmergency, the patches/nodes are recreated and executed. Compositions can contain many different types of patches. Some of the simple patches may load an image, display an image or perform a simple mathematical operation, while some of the more complicated patches can execute Javascript code, execute an OpenGL shader, or send OSC messages over a network. Because they are essentially a set of instructions that is executed (rather than played sequentually like videos are) they can be programmed to react to certain things (e.g. in MixEmergency you can have Quartz Compositions that react to the record velocity), and may produce different output every time you run them. It also means that they don't have a fixed frame rate.
