There is not such thing as a totally silent generator because after all there is an engine that is running and producing electrical power. What does happen is, these manufacturers of power generators will sometimes invest money in designs and materials that help reduce the noise through the engine or with sound dampening products. So when people talk about silent generators, they are really talking about noise reduced generators. There are some really well designed generators with good noise levels.
My first recommendation to people who have never brought a power generator is to ask someone who has one and go around and listen to how it sounds. For really bad designed generators, you can notice the difference at the engine sounds more like a lawnmower and can be very annoying not only to the owners but to the neighbors. If you do not know anyone with a generator, consider a generator with a noise level under 70 dB at 7 meters. This is around the average for many central AC units and should meet most municipal noise pollution laws. A good silent generator should have noise levels around this level or lower using sound dampening techniques.
Silent generators are also great for RV and marine vehicles. Because the vehicles are more enclosed and noise is more of a bother to the individuals in them. No one wants a noisy generator while trying to enjoy a boat ride or camping. A silent generator really solves this problem by lowering the noise level enough to talk over. Onan's MicroQuiet series is a good example offering really low noise levels for RV vehicles. There are a lot of other manufacturers as well that offer either quiet models or special sound shields or additions to lower the overall noise levels of their generators.
Many applications of generators also require quiet noise levels. Many municipalities and home owners associations have rules regarding the amount of noise pollution. These include how long lawn mowers and other noisy tools can be run. The same rules apply to generators and having a noise reduced generator that meets these standards is not only an option but a must. Many parks and other recreational areas have similar noise rules as well and quiet RV or marine generators will insure no problems arise from their use.