Based on excerpts from Section 2 of Nuclear Weapons Frequently Asked Qustions by Carey Sublette.
The key idea in implosion assembly is to compress a subcritical spherical, or sometimes cylindrical, fissionable mass by using specially designed high explosives. Implosion works by initiating the detonation of the explosives on their outer surface, so that the detonation wave moves inward. Careful design allows the creation of a smooth, symmetrical implosion shock wave. This shock wave is transmitted to the fissionable core and compresses it, raising the density to the point of supercriticality.
Implosion can be used to compress either solid cores of fissionable material, or hollow cores in which the fissionable material forms a shell. It is easy to see how implosion can increase the density of a hollow core - it simply collapses the cavity. Solid metals can be compressed substantially by powerful shock waves also though. A high performance explosive can generate shock wave pressures of 400 kilobars (four hundred thousand atmospheres), implosion convergence and other concentration techniques can boost this to several megabars. This pressure can squeeze atom closer together and boost density to twice normal or even more (the theoretical limit for a shock wave in an ideal monatomic gas is a four-fold compression, the practical limit is always lower).
The convergent shock wave of an implosion can compress solid uranium or plutonium by a factor of 2 to 3. The compression occurs very rapidly, typically providing insertion times in the range to 1 to 4 microseconds. The period of maximum compression lasts less than a microsecond.
A two-fold compression will boost a slightly sub-critical solid mass to nearly four critical masses. Such a solid core design was used for Gadget, the first nuclear explosive ever tested, and Fatman, the atomic bomb dropped on Nagasaki. In practice hollow core designs also achieve greater than normal densities (i.e. they don't rely on collapsing a hollow core alone).
In addition to its major objective of achieving supercriticality, compression has another important effect. The increased density reduces the neutron mean free path, which is inversely proportional to density. This reduces the time period for each generation and allows a faster reaction that can progress farther before disassembly occurs. Implosion thus considerably increases a bomb's efficiency.
The primary advantages of implosion are:
a. high insertion speed - this allows materials with high spontaneous fission rates (i.e. plutonium) to be used;
b. high density achieved, leading to a very efficient bomb, and allows bombs to be made with relatively small amounts of material;
c. potential for light weight designs - in the best designs only several kilograms of explosive are needed to compress the core.
The principal drawback is its complexity and the precision required to make it work. Implosion designs take extensive research and testing, and require high precision machining and electronics.