Why is change in the participation rate important in assessing the impact of changes in the unemployment rate?
When you say "participation rate," I assume that you are asking about participation in the labor force. If so, changes in the participation rate are important because they can cause the official unemployment rates to be misleading.
At times, unemployment rates can fall even though fewer people are working. As people stop looking for work, they drop out of the labor force. They are typically called "discouraged workers" and are not counted as unemployed even though they do not have jobs. If this happens, the unemployment rate will misstate the actual amount of change that is going on in the economy. The unemployment rate might, for example, decrease even though no more people are working. This would make it look like the economy is improving when it is not.
In this way, changes in participation in the labor force can mislead us about the actual impact of changes in the unemployment rate.