Volume bound charge and volume bound current $\rho_b$ stands for volume bound charge and $\vec{J}_b$ stands for volume bound current. I have learned that $\rho_b=-\nabla\cdot\vec{P}$ and $\vec{J}_b=\nabla\times\vec{M}$. Does that mean if the "polarization" in the material is uniform then $\rho_b$ is zero? And $\vec{J}_b$ is zero if the "magnetization" in the material is uniform?
 A: Yes if the polarisation is uniform, in this case the divergence of the polarisation or the curl of the magnetization is zero.
But, and this is important, areas with non-zero (uniform) polarisation are limited in space. Think of a rod magnet. It covers a limited volume in space. Or a condensator filled with a dielectrical material. It is of limited size.
Therefore at (some) borders of these zones neither divergence of polarisation is nor the curl of the magnetisation is zero.
Therefore at the border where the metal plates of the condensator hit the dielectricum the divergence of polarisation is non-zero.
This means at the border between the condensator metal plates and the dielectric material there is a polarisation charge which gives rise to the electrical field inside the condensator even though there is no free charge in the condensator. A polarisation charge is bound. It cannot move. Therefore it is not free. But it is nevertheless the source of an electrical field. In order to avoid any ambiguity, we assume for this example that the polarisation of the dielectric material is perpendicular to the metal plates of the condensator.
Something similar happens with the curl of magnetization of the rod magnet  which we here imagine as a little cylinder. Furthermore we assume that the direction of the magnetisation is along the cylindrical axis of the rod magnet.
The curl of magnetization is above all non-zero on the  cylindrical surface of the cylinder-shaped form of the rod magnet, whereas it stays zero at the flat end surfaces (i.e. the poles) of the rod magnet.
In order to get the bound magnetic charge at the poles (the flat end surface of the rod magnet), the divergence of the magnetisation has to be computed.
By the way, $\mathbf{J}_b$ is not a charge it is a current.
