When a rigid body moves in such a way that all its particles move along parallel paths, its motion is called translational motion. Since all the particles execute identical motion, its centre of mass must also be tracing out an identical path. Therefore, the translational motion of a body may be characterised by the motion of its centre of mass.
Ma = Fext
The motion of a rigid body in which all its constituent particles describe concentric circular paths is known as rotational motion. The rotational motion can be obtained by keeping a point of the body fixed so that it cannot have any translational motion. For the sake of mathematical convenience, this point is taken to be the Centre of Mass. The rotation is then about an axis passing through the Centr of Mass.