What does it mean that a magnetic field's flux vanishes through any closed surface? I'm reading the Britannica guide to Electricity and Magnetism, and I came across the following quote:

A fundamental property of a magnetic field is that its flux through
  any closed surface vanishes.

Can someone explain this in simpler terms?
Source 
 A: 
Can someone explain this in simpler terms?

Typically, the closed surface is a mathematical surface (Gaussian surface) which simply defines an 'inside' and 'outside'.
Since, as far as we know, there are no magnetic charges from which magnetic field lines start or end, any magnetic field line entering must exit through the surface; any magnetic field exiting must enter through the surface.

Thus, the number of field lines entering equals the number of field lines exiting and the flux of the magnetic field through the surface is zero.
A: If the flux in and out of a surface cancles, there is no need for magnetic charge in which field lines can end or start (e.g. like the electric charge). One expresses this like
$$ \nabla \cdot \vec{B} = 0 $$
wich means
$$ 0 = \int_V \nabla \cdot \vec{B} ~ dV = \int_S \vec{B} \cdot d\vec{S} $$
where $S$ is the surface of the volume $V$.
A: There are no magnetic monopoles. i.e. Unlike electric field flux, there are no sources or sinks of magnetic flux.
Therefore the amount of flux entering any closed volume must equal the amount exiting.
