  Copper borate Cu$_3$(BO$_3$)$_2$ is a complex compound with a layered
crystallographic structure in which the Jahn-Teller active and magnetic copper
Cu$^{2+}$ ions occupy sixteen nonequivalent positions in the unit cell
displaying controversial magnetic behavior. In this paper, we report on the
infrared and Raman spectroscopic studies of the lattice dynamics and the
electronic structure of 3$d^9$ copper states below the fundamental absorption
band. The lattice dynamics is characterized by a large number of phonons due to
a low $P\overline{1}$ space group symmetry and a large unit cell with Z=10.
Unusually rich set of phonons was found in the low-energy part of the infrared
and Raman spectra below 100 cm$^{-1}$, which we tentatively assign to
interlayer vibrations activated by a crystal superstructure and/or to weak
force constants for modes related to some structural groups. Several phonons
show anomalous behavior in the vicinity of the magnetic phase transition at
$T_N$=10 K thus evidencing magnetoelastic interaction. No new phonons were
found below $T_N$, which excludes the spin-Peierls type of the magnetic
transition. In the region of electronic transitions, a strong broad absorption
band centered at $\sim$1.8 eV is observed, which we assign to overlapping of
transitions between the 3$d^9$ states of Cu$^{2+}$ ions split by the crystal
field in nonequivalent positions. The fundamental charge-transfer absorption
band edge has a complex structure and is positioned around $\sim$2.8-3.0 eV.
