If the divergence $$\nabla \cdot \boldsymbol{F}$$ of a vector field $$\boldsymbol{F}$$ vanishes at the location $$(x,y,z)$$:$\nabla \cdot \boldsymbol{F}(x,y,z) = 0$then at the location $$(x,y,z)$$ there is neither a source nor a sink of the vector field $$\boldsymbol{F}$$. If this point is enclosed by an arbitrary surface, then the vector field 'flows' out of the surface as much as into it. Or the vector field is zero.