Hysteresis is a situation "where one-time disturbances permanently affect the path of the economy." (Romer Advanced Macroeconomics page 471)
In unemployment, hysteresis can occur from as a results of type described by Insider-outsider Models. Deterioration of skills from unemployed people lessens their human capital and can exacerbate the effect. Another source is "labor-force attachment." Unemployed workers must adjust their standard of living to a lower level, and they can get used to it and not try as hard to achieve the higher previous level. Longer periods of unemployment also reduce the stigma and hence labor supply may be permanently lower after demand returns to normal.
Hysteresis is possible in Europe. Once unemployment spiked, people adjusted to lower levels of living, the stigma for being unemployed declined, and their skills declined. This contributes to a higher rate of unemployment.