Imagine a virtual world that contains many moving rigid bodies. For each body, think about its degrees of freedom (DOFs), which corresponds to the number of independent parameters needed to uniquely determine its position and orientation. We would like to know the complete list of parameters needed to put every body in its proper place in a single time instant. A specification of values for all of these parameters is defined as the state of the virtual world.
The job of the physics engine can then be described as calculating the virtual world state for every time instant or ``snapshot'' of the virtual world that would be needed by a rendering system. Once the state is determined, the mathematical transforms of Chapter 3 are used to place the bodies correctly in the world and calculate how they should appear on displays.