what is the current explanation for the formation of cosmic voids? Why aren't galaxies distributed evenly in space, but instead form those sponge-like structures, with huge voids between filaments?
Void formation is due to baryon acoustic oscillations. These can be thought of as fluctuations in the dense matter in the early stages of the universe; they became anisotropies, which can be seen in the cosmic microwave background. The fluctuations grew, until they hit the 150 Mpc scale, which correlates nicely to the sizes of voids in the universe today.

There's an interesting section (4.2) in this paper by Robert Brandenberger, which gives a mathematical treatment of how fluctuations of all kinds grew in the early universe. There is a better version of the explanation in Zeldovich (1972), which in fact puts forth the theory. The number density (if you'll pardon the pun) is lesser in that latter, but the former has a good overview, as it is meant to be a broad summary.

The simple explanation is that tiny fluctuations grew over time to become enormous structures.