Solve high-frequency oscillation problems on your quad by filtering low-frequency noise out before it gets to your flight controller.
The transition between hard and soft materials provides vibration absorption. By squeezing a soft piece of silicone between the motor and the frame, certain vibration frequencies will get attenuated. Without soft mounting the vibration noise may saturate the gyro reading, making it impossible for the gyro to distinguish signal from noise. The end result is high frequency shakes or spastic movements of your quad - either at full throttle or mid throttle - that remain regardless of your PID values.
In most cases, soft-mounting the flight controller or motors will get rid of these issues. With the TBS soft-mount silicone kit, you'll get everything necessary to improve the flight handling of your quads.
When soft-mounting, you need to be aware of the advantages as well as the disadvantages. In essence, soft-mounting is a vibration filtration technique. Every kind of filtering introduces latency. By allowing the motors to move just a tiny bit, we create a slower response from the quad. It will manifest itself as a "smoother" response to your control inputs, but also mean that your muscle-memory may need to go through some minor re-adjustment. The downsides can be considered minimal, just don't expect to have your cake and eat it too, is what we're saying.