A "ducker" is a system that turns a signal down to 0 when it's below a given threshold. This is also frequently called a "noise gate" in audio engineering, because it acts as a doorway that closes out unwanted low-level ambient noise and lets through only the louder, more desired signal. It's useful for suppressing unwanted low-level audio, such as in a cell phone transmission when the user is not talking, or, more to the point for musical purposes, as in a microphone signal when the musician is not playing.
The example demonstrates two methods. This first one uses smoothing to create a ramp on and off instead of an instantaneous switch on and off. This second one waits a certain amount of time before it begins the release ramp, and if the input signal goes back above the threshold during that time it cancels the release (the default amplitude threshold being -40 dB).
The rampsmooth~ object is useful for smoothing MSP signals, a sort of lowpass filter, especially appropriate for smoothing out overly sudden changes in control signals. The left part of this patch demonstrates the fact that internally rampsmooth~ is just doing linear interpolation. Whenever the input signal changes, rampsmooth~ heads toward that value from wherever it currently is, using the specified number of samples (depending on whether it has to increase or decrease) to get there.