OK, so I don't think the article is claiming that it is a place "without matter", but that it is a large region of space where the density of matter is lower.
The original research, published in 2007, suggests that a lack of radio sources seen in a particular direction coincides with a "cold-spot" that is seen in the cosmic microwave background by WMAP (which has since been confirmed by Planck). They calculate that if the void were completely empty it would need to be about 280 Mpc across and at redshifts $z\leq 1$.
Galaxies certainly could be seen on the other size of this void. Many of the galaxies in their survey must have considerably higher redshifts and are more distant.
The cold spot could be caused by such a void, because light is redshifted as it travels through gravitational fields. The Sachs-Wolfe effect, as it is known, causes large scale perturbations in the cosmic microwave background as light travels from the distant past, when the CMD was generated, to us in the present day. It is argued that a large void that is comparatively empty of both visible and dark matter, but which has dark energy. The way it works is that photons works against gravity to enter a void, loses energy, but then gain back some of that energy as it leaves the void. However, the expansion of the universe means that in the time taken to cross the void the amount that is regained is not as much as was lost in the first place.
"What if a black hole were to appear"? Not clear what you mean by this. Black holes are black, you wouldn't necessarily see them, however if the "void" or lack of radio galaxies was compensated for by an equivalent amount of mass that was for some reason invisible then it would not explain the CMB cold spot.
The idea of a "supervoid" causing the CMB cold spot has also been supported by other surveys of extragalactic sources (Szapudi et al. 2015), but you are correct that the size of this void is difficult to understand in terms of current cosmological assumptions.