The Nyquist plot (one is shown in the video above) is a very useful tool for determining the stability of a system. It has advantages over the root locus and Routh-Horwitz because it easily handles time delays. However, it is most useful because it gives us a way to use the Bode plot to determine stability. We can not only use the Bode plot to determine stability, but it also gives us insight on how to improve the stability of a system. To fully understand the Bode plot based methods for determining stability it is important to first understand the Nyquist plot. This presents some difficulties because the Nyquist plot uses some rather abstract mathematical techniques. These web pages try to demystify the process by starting with some simple examples (with animations) and then proceeding to more complicated examples. The treatment given here is not meant to be mathematically rigorous (it does not even use contour integration in the complex plane), but rather to give engineering students an intuition for what the Nyquist plot represents, and how it is used to determine the stability of a system.
The next several documents describe the Nyquist plot.