Mark Thoma explains the difference between cyclical, structural, and frictional unemployment:

As I noted in a previous post, economists define three types of unemployment: frictional, structural, and cyclical:

Frictional unemployment is defined as the unemployment that occurs because of people moving or changing occupations. Demographic change can also play a role in this type of unemployment since young or first-time workers tend to have higher-than-normal turnover rates as they settle into a long-term occupation. An important distinguishing feature of this type of unemployment, unlike the two that follow it, is that it is voluntary on the part of the worker.

Structural unemployment is defined as unemployment arising from technical change such as automation, or from changes in the composition of output due to variations in the types of products people demand. For example, a decline in the demand for typewriters would lead to structurally unemployed workers in the typewriter industry.

Cyclical unemployment is defined as workers losing their jobs due to business cycle fluctuations in output, i.e. the normal up and down movements in the economy as it cycles through booms and recessions over time.

In a recession, frictional unemployment tends to drop since people become afraid of quitting the job they have due to the poor chances of finding another one. People that already have another job lined up will still be willing to change jobs, though there will be fewer of them since new jobs are harder to find. However, they aren’t counted as part of the unemployed. Thus, the fall in frictional unemployment is mainly due to a fall in people quitting voluntarily before they have another job lined up.

But the drop in frictional unemployment is relatively small and more than offset by increases in cyclical and structural unemployment.