The chalk particles embed themselves into the small pores on the surface.
Although a chalkboard seems smooth to the touch, it is quite rough at the microscopic level, with <em>pores</em> that reach below the surface.
When you drag chalk across the board, friction causes small particles of chalk to rub off onto the surface.
If you leave the markings for a long time, some of the chalk particles will work their way into the pores.
A brush will remove the surface particles, but <em>it will not be able to get at the particles in the pores</em>.
