Question

what is an extended object

Answer 1

Sometimes you can treat an object as a 'point mass'. That means its actual dimensions (length, height diameter or whatever) are small enough to be unimportant and the object can be approximated to a particle of negligible size. In this case the object's centre of mass is simply the same as the position of the mass. 

But if the size of the object has one or more important dimensions (e.g a stick of length L, or a disc or radius r, or a solid of some shape) the object is described as an extended body. The centre of mass is one of the infinite number of points inside the object.