The Nyquist criterion determines closed-loop stability from the complex frequency response of the open loop.

For negative feedback with loop transfer function $L(s)$, closed-loop poles are zeros of

$$1+L(s),$$

so the critical point in the $L$-plane is

$$-1+0i.$$

Let $P$ be the number of poles of $L(s)$ in the open right half-plane and let $N$ be the net number of clockwise encirclements of $-1$ made by the Nyquist plot. Then the number $Z$ of closed-loop right-half-plane poles satisfies

$$N=Z-P.$$

Closed-loop stability requires $Z=0$. Therefore an open-loop stable system with $P=0$ must make no net encirclement of $-1$, while an open-loop unstable system requires the corresponding counterclockwise encirclements so that $N=-P$.

Nyquist gives a global frequency-domain stability test and explains why gain and phase margins measure distance from the point $-1$.