Note that the range of integration has changed from $V$ meaning over the volume to $dV$ and that the variable of integration has changed from $\text{d}^3x$ to $\text{d}S$.

It means an integral over the surface that bounds the volume.

The closed curve over the integration signs imply that the surface must be closed.

This expression is an application of what physicist tend to call Gauss's Law, and mathematicians tend to know as the divergence theorem.

Note that the range of integration has changed from $V$ meaning over the volume to $\partial{V}$ and that the variable of integration has changed from $\text{d}^3x$ to $\text{d}S$.

It means an integral over the surface that bounds the volume.

The closed curve over the integration signs implies that the surface must be closed.

This expression is an application of what physicist tend to call Gauss's Law, and mathematicians tend to know as the divergence theorem.