The term "unsupported chamber" is bit of a misnomer. Its not limited to pistols, or to specific calibers. Its a characteristic of the loading system of semiautomatic firearms (not just pistols). When a round is loaded, it travels from the magazine, up a feed ramp, in to the barrel (the chamber) where it comes to a rest until the gun is fired.
Some barrel designs expose a bit more of the rounds casing than others. The ones that expose more are referred to as "unsupported chambers"
Here are some pictures from a 1911 enthusiast that can help illustrate.
With a frame loaded 1911, the round travels up a ramp formed by the frame, and a cutaway in the lower part of the barrel.
With a ramp loaded 1911, there is a ramp that guides the bullet in to the barrell. As a result, the barrel does not have the same cutaway on the bottom, and offers a few more millimeters of more support to the loaded cartridge. These difference in this support to the cartridge is the differentiation between a "supported chamber" and an "unsupported chamber".
http://38super.net/Pages/supported.html
The extra support is more expensive to manufacture, but can can make a difference in the accuracy of the firearm at longer ranges. One wouldn't find a sniper rifle, for example, with an unsupported chamber, but there are shorter range rifles that can be found without a feed ramp that offers a fully supported chamber.
At shorter ranges, the mechanical differences of an unsupported generally not a key factor in accuracy or ease of load, and are often easier to manufacture.
Both loading mechanisms are safe. A "kaBoom" or case rupturing is caused by ammo that is not in spec, or by a barrel obstruction (most common cause is not properly cleaning the gun after its been fired), or both.