Assume you are in a perfect hover, disc level, no wind.
No cyclic is applied, no flapping anywhere.
Along comes a rogue puff of wind, for convenience it is from the front. There is now a relative wind, and an advancing side and a retreating side.
The advancing side has a higher relative airflow, the lift generated is proportional to the square of the wind velocity, so it develops more lift than the retreating side. The force generated makes the blade start to fly up - the balance between centrifugal force and rotor lift has been upset. As it flies upwards, the induced flow component increases until it reduces the angle of attack and thus the lift, until the balance is restored again.
On the retreating side, as well as being pushed down by the teetering effect of the advancing blade flying up, there is less relative airflow, so the blade falls downwards. As it does so, the induced airflow is reduced, increasing the angle of attack and the lift, until the balance is restored between rotor lift and centrifugal force. But this flying up and flying down takes time - the force on the blade is instant, but acceleration up or down takes time to establish itself - about 90 degrees - and it is likened to the precessional property of a gyroscope, to allow us simple pilots to understand what is happening.
The end result of this puff of wind is that the blades have flapped to equality, but now the disc is tilted up at the front and down at the back. Where is the rotor thrust now pointing? Backwards! So, the aircraft, which was in a steady hover before, will now move backwards away from the wind.
It moves backwards more and more, until there is now a relative wind from behind. The disc flaps away from that, but the pendulous effect of the fuselage hanging under the disc makes the reversal of direction a bit more pronounced, and the disc is now tilted even further down to the front.
This is the start of dynamic instability.
All this time, the cyclic has been held in a neutral position. The pilot decides he doesn't want this to continue, so he stops the oscillation, and returns to a steady hover in the new headwind. The fuselage is stationary, but the disc is tilted forward to overcome the wind, and the cyclic feathering all around the disc is stopping the disc from flapping to equality. The equality of lift is achieved by the cyclic feathering.