The space around a magnet where the force of the magnet can act
is the space occupied by the magnetic field. Alternatively we say
that the magnetic field acts in the space around a magnet.
That is a very qualitative statement with little predictive
value.
More predictive value is contained in a statement that the
strength of the magnetic field at any position in the vicinity of a
magnet is measured by the torque which is exerted on a small magnet
moment (compass) place in the vicinity of a magnet. This, recorded
with the direction the test compass points is actually a mapping of
the magnetic field of a magnet.
As a side note, if carefully measured one discovers that
strength of the field around a magnet decreases as the inverse cube
of the distance when far from the magnet. The field is mostly in
the volume near the magnet but the weakening field continues to
exist at all distances from the magnet.
