How is the business cycle related to employment and inflation?

The business cycle looks like a roller coaster. At the lowest point there is a trough, then an expansion to a peak, and then a downturn to the next trough. In a downturn or a recession, demand slows down, and workers are laid off. In order to increase employment, the government may enact either fiscal or monetary stimulus policies, or perhaps both. Those policies most often have the intended effect of stimulating aggregate demand so that laid-off workers are called back to work.

However, they also have the unintended effect of causing inflation (an increase in the general price level) in the economy. If the inflation goes very high or lasts for an unacceptably long time, then the government will reverse policies and try to contract or slow down the level of growth. If that works, it will decrease demand, and control inflation as intended, but it may also cause a decline in employment. That is how the cyclical nature of the economy happens over time.