  We use a combination of optical spectra, first principles calculations, and
energy dependent magneto-optical measurements to elucidate the electronic
structure and to study the phase diagram of Ni$_3$V$_2$O$_8$. We find a
remarkable interplay of magnetic field and optical properties that reveals
additional high magnetic field phases and an unexpected electronic structure
which we associate with the strong magneto-dielectric couplings in this
material over a wide energy range. Specifically, we observed several prominent
magneto-dielectric effects that derive from changes in crystal field
environment around Ni spine and cross-tie centers. This effect is consistent
with a field-induced modification of local structure. Symmetry-breaking effects
are also evident with temperature. We find Ni$_3$V$_2$O$_8$ to be an
intermediate gap, local moment band insulator. This electronic structure is
particularly favorable for magneto-dielectric couplings, because the material
is not subject to the spin charge separation characteristic of strongly
correlated large gap Mott insulators, while at the same time remaining a
magnetic insulator independent of the particular spin order and temperature.
