[Ref ACE The Technical Pilot Interview, Pilot’s Handbook of Aeronautical Knowledge, FAA-H-8083-25B Page 5-20]
Dutch roll is a coupled lateral/directional oscillation (combination of yawing and rolling motions) – the nose of the aircraft making a figure eight on the horizon;
Notes: V-tail design are also more susceptible to Dutch roll tendencies
The sweep wing design make the aircraft has a more significant lateral stability than directional stability – roll is much more noticeable and unstable.
When a yaw is induced, either by a disturbance or by a commanded input, the outer wing travelling faster and more straight to the relative airflow and so the outer wing produces more lift and increases its angle of attack. Meanwhile, the inner wing travelling relatively slower and less straight to the relative airflow, so the inner wing produces relative less lift. The difference in lift causes the aircraft bank. The bank could cause the angle of attack of the outer wing over the critical AoA and so it stalls and drops. The wind drops causes a yaw to the dropped wing and above principle repeat again and again – the dutch roll happens.
Notes: “Spiral instability” is more desirable than “Dutch roll tendencies” in aircraft design.