It's quite obvious that it isn't simply a crater, but what is it then? Is it a caldera filled with extremely dark matter, like the Wau Namus, that appears as a hole in the deserts of Lybia? Is it a lake of oil? Is it caused by sandworms?
The Sun's angle wasn't too low when the image was taken, so the fact that we can't see the walls means it can't really be a pit. The most likely explanation is that it is a sort of skylight, a hole in the ceiling of a cave, that also occur on Earth. If the cave is very deep and large, the illuminated floor can't be seen from exactly above, and we just see a black hole instead.
The hole - and 6 others - lie on the slopes of one of the largest volcanoes in the Solar System, Arsia Mons. (More context here, but Arsia Mons is so large it still won't fit on the image). So probably the hole is on the ceiling on a horizontal lavatube.
Infrared measurements also confirmed that they should be caves indeed, as they appear colder than their surrounding during daytime, while warmer in the night.
Here's another feature, from a different region of Mars. This was interpreted as horizontal lavatube, the roof of which collapsed, except for a short section (forming a natural bridge):
In the past weeks, the HIRISE team were now able to make another close-up image of Jeanne, with different illumination:
Here it looks more like a vertical shaft, or just a deep pit. It has a diameter of about 150 meters, and a depth of least 78 meters. Luckily there are chances of peeking even deeper, when the Sun climbs higher on the Martian sky in a few months.