Principles of atomic bombs

To explode, the bomb must first be imploded: compress a subcritical spherical fissionable mass (a ball of normal density uranium and other metals) with specially designed explosives. Implosion is the detonation of explosives on the outer surface, instead of the inner surface, which causes the detonation/shock wave to move inward. The engineers working on the bomb had to carefully design a smooth, symmetrical implosion setup so that the shock waves would reach each part of the core at the same time, and that was a very difficult task. Once the shock wave is transmitted to the fissionable core it compresses the core and raises the density to the point of superciticality. Which then leads to a great explosion, which in the case of "Fat Man" is equivalent to 10,000 tons of TNT. Essentially what is happening here is that the fissionable mass is crushed to a great density, and once the mass has reached that supercritical density it goes boom!
There are four main problems that must be taken care of for an atomic bomb to explode. They are all related with creating a fission chain reaction:
The fissionable material must be kept in a subcritical state before detonation.
The fissionable material must be brought into a supercritical state while keeping it free of neutrons. Otherwise most of the fissionable mass would be used up and it would not generate a large explosion (if any). The neutrons must be added to the critical mass when it is at maximum supercriticality, meaning at the most "explosive" point. This can be compared to releasing a rubber-band when it is fully stretched so it will travel with the most speed.
The fissionable mass must be kept together until a large amount of it has gone through fission, making it efficient. If the fissionable mass does not stay together, the fission reaction would immediately be stopped. When the atomic nuclei in the center of an atomic bomb, which is composed of fissile materials, are split, an enormous amount of energy is released as dangerously high levels of heat and radiation. Atomic bombs use this energy as a weapon for killing.

Other explanation: When a single neutron strikes the nucleus of a fissile material such as uranium 235 (or plutonium 239), two or three more neutrons are released. When those neutrons are ejected, enormous energy is released. The flying neutrons then hit other nuclei of the uranium and cause them to split in a similar manner, releasing more energy and neutrons. When this fission spreads, a huge amount of energy is generated instantaneously.
Estimated damages of atomic bombs:

Atomic:    (-800 m): Deadly
   	    (-1000 m): Deadly for 50% of all persons
 	    (-2000 m): Shock- and Heatwawe, Neutrons- and Gammaemission
 	   (-2200 m): Destruction of buildings
 	   (-3000 m): Heavy fires
Neutronic: (-200 m): Destruction of buildings
           (-800 m): Deadly within 1-2 days
           (-1000 m): Deadly within 4-6 days
           (-1200 m): Mostly deadly within a few weeks
           (-1400 m): Deadly for 50% of all persons
           (-3000 m): Neutronic emission

This is a model of a basic Teller-Ulam atomic bomb.
Vocabulary explanations