a rigid body

A rigid body is an idealized extended object whose shape never changes: the distance between any two of its points stays fixed no matter how the body moves. Think of a hammer, a spinning top, or a planet treated as perfectly stiff. In Volume I you learned to treat objects as point particles; a rigid body is the next step up, an object that can also spin and tumble, but that never stretches, bends, or squashes.

The rigidity constraint is powerful: it collapses the astronomical number of coordinates of all the atoms down to just six numbers. A rigid body has six degrees of freedom -- three to locate one reference point (usually the center of mass) and three angles to fix its orientation in space. Its most general motion is, by Chasles's theorem, a translation of that point plus a rotation about it. The velocity of any point P is therefore v_P = v_cm + omega x r, where omega is the angular velocity and r is the position of P relative to the center of mass.

You meet the rigid body every time you analyze rotation with real objects rather than idealized particles: gyroscopes, wheels, molecules, tumbling satellites, a diver's twist. It is where the single number 'moment of inertia' from Volume I grows up into the inertia tensor, because a real body's resistance to rotation depends on the axis you spin it about. Remember it is an idealization -- no real material is perfectly rigid, and continuum mechanics (strain and stress) is exactly the theory of what happens when you let the body deform.