Ok, this can get really technical, so I wanted to think about the best way to explain it.
Marble Stability Example
A = Stable equilibrium. The ball moves back towards its equilibrium position when disturbed. If the valley is infinitely deep the system is said to be globally stable.
B = Unstable equilibrium. The ball moves away from its equilibrium when disturbed.
C = Neutrally stable equilibrium. The ball stays wherever it is placed.
D = Metastable equilibrium. The ball returns towards equilibrium as long as disturbances are not too large. The equilibrium is not globally stable because once the ball has crossed the unstable equilibrium (the peak), it is unlikely to return to the stable point.
E = Metastable equilibria with multiple stable states. The ball returns towards one or the other equilibrium depending on which side of the unstable equilibrium it is. The system is globally stable.
What It Means:
If you place a marble on the outer surface of a circular path, a slight nudge will cause it to roll away from its intial position. This is divergent, meaning that it does not very much "want" to return to its initial state. Aircraft that are very sensitive exhibit this same behavior.
If, on the other hand, you place a marble on the interior surface of a circular path, a slight nudge will cause it to initially roll away from its position, but it will "want" to return to its initial position. This is convergent. Aircraft that are sluggish exhibit this behavior.
So, if the I-16 is very sensitive to small input, it will inherently respond quickly and with large magnitude. In order to correct for this, a pilot must compensate for this, in effect providing a dampening effect to the control model. The fact is, the I-16 control model is not actually divergent, but rather extremely "not convergent" In effect, the system has a dampener, but it will take a long time for the pitch oscillations to die out. This is why the I-16 could be flown by hand, and modern fighters can not be flown without 'fly-by-wire' controls. The F-16 and the like all have divergent control models that respond to quickly for a human to control.