What does it mean when a toenail turns black after a minor physical impact?
Would this disappear by itself (it's already over a month)?
What you have is called a subungual hematoma; that's just a fancy way of saying a collection of blood under the nail. It may happen with any kind of direct trauma, including (perhaps the worst?) a broken toe. It is similar to any other injury causing bleeding; the major difference is you can actually see the dark blood because the nail is transparent.
Yes, it will disappear by itself, but as already noted by @JohnP, it will take a long time, as the clotted, thickened blood residue will be pulled towards the tip of the toe at the same rate that your toenail grows.
This is a picture of a subungual hematoma (SUH) after six months of growth:
As you can see, there is a nice, normal nail growing out. I will hazard a guess that this particular injury was a lot like yours by the ridge formed across the top of the new nail. This indicates that the nail was lifted slightly off the nail plate. Also, this is a very slow growing nail.
Your SUH needs no treatment this far out.
As @JohnP noted, if there was significant injury to the growth plate, your nail may be permanently changed: it may be thicker, ridged, shorter, etc. But often this grows out without any problem.
Acute care includes ice and elevation. If very painful, most doctors are capable of trephining the SH under sterile conditions (burning a small hole in the nail through which the blood may escape.) This sounds much worse than it is; in actuality, it provides immediate relief.
Because this was associated with trauma, it is a SUH. However, if it was not associated with trauma, one would need to consider a subungual melanoma, meaning a skin cancer under the nail. These can spread into adjacent soft tissue. Keep it in mind as it grows out; it should be replaced by fresh, unaffected nail.
It's much the same as any other traumatic impact, it's a collection of blood from ruptured vessels. In the skin, it appears as a bruise. When under the nail, it appears as a black shape, usually a crescent.
If the amount of blood is significant, or if the pressure of it causes pain, you should have it checked out by a podiatrist. It is also possible that if the trauma was severe, that there can be a risk of infection.
It will last quite a long time, as the nails (both fingers and toes) are relatively slow growing (average 3mm/month). It is possible that you will lose the nail, although after a month that is less likely. It is also possible that the nail will not grow back in a normal shape, as you may have caused trauma to the nail bed. The black shape (old, clotted blood, actually) will move out with the growth, and may possibly cause nail splitting and separation from the bed in the affected area. Eventually it will reach the end of the nail and can be removed.
While not urgent after a month, there are possibilities of complications, so if you notice any pain, further discolorations or odors, have it checked by a professional.