Underground there is more ambient hard radiation. Radon gas is a prime example and a major source for radiation exposure in subterranean spaces. The Drow use this radiation to supplement their metabolic activity in the same manner as radiotrophic fungi.
. Robertson et al. studied black yeast (Wangiella dermatitidis)
subjected to low-dose ionizing radiation.  They wanted to deduce
the impacts of chronic radiation on the melanin-containing yeast
(recall that melanin is the pigment that results in human skin color),
as well as melanin-lacking yeast. They discovered that radiation led
to increased survivability in the melanin-containing fungi, as they
were able to absorb more nutrients and export more toxic metabolites
from their cellular systems. The scientists even found that fungi were
able to safeguard their DNA and utilize ionizing radiation as energy
for DNA repair in some extreme cases.  Dadachova et al. also noted
that while melanin-lacking fungi grew better in non-irradiated
environments, this observation quickly reversed in the presence of
radiation, with melanin saturated fungi actually increasing rapidly in
dry weight in the presence of continual radiation.
This growth can be at least partially explained by melanin's ability
to catalyze an oxidative-reduction reaction typical of cell
metabolism. According to Dadachova et al., the electron transfer
properties of melanin in the NADH oxidation/reduction reaction
sequence necessary to supply cellular energy increased 4-fold after
prolonged exposure to radiation. Furthermore, even melanin-containing
fungi cells subjected to limited nutrient conditions responded by
growth when exposed to radiation as compared to their non-melanized
Maybe the Drow use this for energy. Better would be for the melanin catalyzed oxidation /reduction to serve the same role UV light does on the surface - UV hitting the skin makes vitamin D for humans. In circumstances where UV light on the skin is scarce (people wear a lot of clothes, or days are short) humans evolved paler skin to maximize the ability to capture what UV there was.
Assuming human-type vitamin D metabolism in the Drow, they get essentially no UV light. They instead use melanin pigment (the only human pigment) to capture hard radiation to make vitamin D. The Drow are actually cave adapted albinos who secondarily acquired the ability to capture hard radiation energy via pigment, which is why they have white hair and pink eyes but skin that is nearly coal black.
Thinking more about what phenotype would result from this use of melanin, it would not look like humans exposed to UV. UV stops at skin, but hard radiation penetrates tissues. The drow would therefore have melanin through and through - not just on skin but also interior tissues and organs, blood, sclera and everywhere. Their sclera would be black and their blood would be black. This could happen if there were an organ that secreted melanin into the blood stream - occasionally this sort of global pigmentation can happen to people with widely metastatic melanoma - depicted.
Diffuse cutaneous melanosis in metastatic melanoma
Hair does not have a blood supply and so would stay white. Apparently irises are unaffected too so they would stay albino red.