Verdict- Misleading. This claim has been making it's rounds on Facebook again recently, although it's been around for many years. A quick search brings up literally hundreds of sites in several different languages within the last 12 years about this. Most of them have the same wording, with no real information on any of them, and no pictures of any other holes than the one pictured here. There are plenty of hypothesis however, ranging from them being natural sinkholes to claims of them being samples of earth taken by aliens. One claim even went as far as saying that they are dug from below by "mole people." Looking at the hole you can clearly see it was drilled by the horizontal marks on the walls, which eliminates the chances that it is a sinkhole or a naturally occurring phenomenon.
The pictures accompanying the claim (more here taken around 10 years after the initial discovery) sheds some light on this, and although they don't solve the "mystery", they do paint a different scenario that what is claimed. The pictures you see are from a hole found in Kharkov, Ukraine that was discovered in the late 1980's by a sheep herder out tending his flock by the name of Pyotr Malinkin. He supposedly claims the hole was not there the day before, and had appeared overnight.
So, now we know that this hole is not out in the middle of some dense uninhabited forest as is claimed. We know the area easily has the capabilities to make such a hole without any problems. We know it wasn't naturally occurring. We also know that the hole isn't really all that deep from the rest of the pictures, although you still wouldn't want to fall in to it. All in all, it pretty much comes down to it either being an old well, or some company came along drilling test holes in search of resources, and didn't find any. Either way, if the hole was filled back in improperly, most of the fill would have washed out over time from heavy rains, exposing it once more.
So what about the rest of these "holes" that are claimed to be appearing all over the place? There doesn't seem to be much, if any, evidence of them even existing. According to the locals near the one the pictures were taken of, there is supposedly another one nearby that is much larger, but no one has been able to find it.
Kharkov, Ukraine Industry
Mysterious Holes, (English Russia)
uh.ru (More pics/ another claim in Russian)