Dutch roll is characteristic of aircraft with stronger lateral stability than directional stability.
If the aircraft encounters a disturbance causing yaw (the pilot can do this by pushing a rudder pedal), the outer, faster travelling wing will rise due to lift increase, much more markedly so if a swept wing. There is no significant change in wing angle of attack, but as the yaw continues, the 'weak' fin encounters an increasing angle of attack, and returns the aircraft towards normal, but causing greater lift on the opposite wing, causing a reversal in roll direction as the aircraft commences a yaw in the opposite direction....until the fin encounters an increased angle of attack from the opposite direction, and returns to normal, overshoots into another yaw in the original direction, and so it goes on.
Some aircraft will self correct after a few oscillations, whilst others become more and more divergant to the point of structural failure.
As a historical note, I believe that the term "Dutch Roll" originated from a Boeing engineer's observation of the likeness between the Dutch girl's swivelling bottoms whilst skating, and the new unstable condition discovered on the B47.