Business cycles refer to the rise and fall of economic growth that an economy experiences over a period of time. Business cycles are extremely important in economics because economists try to predict economic events and the business cycle shows the direction where the economy is heading. A general description of the business cycle is that it shows the changes in the demand side of the economy, measured by GDP:
GDP = C + I + G +NX
The business cycle is typically seen as a sinusoidal relationship between real GDP and time that trends upwards (for most countries). This relationship outlines the differences between short and long run economic growth. In the short run, we can see that the economy experiences many booms and busts which are a natural part of the growth of an economy. We can remember the many recessions in the near past such as 2008, 2001, 1990, 1981, etc and their corresponding economic expansions to represent the ups and downs of the business cycle. Nontheless throughout such a 30 year period there has been a contant upward growth in real GDP. That is to say if you compared the average GDP of this decade to the 80's, it is greater. This is the long term tredn of an economy and is envisioned as a trend line that cuts through the sinusoidal business cycle.
The goal of policy makers is to reduce the magnitutde of the business cycle and keeping the booms and busts as close to the long term trend as possible. This is known as stabilising the business cycle. The difficulty arises in determining and which point of the business cycle an economy is at. To solve this policy makers try to use various economic indicators such as unemployment rates, investment rates, savings rates, etc.