An example of an automatic stabilizer would be the issuance of unemployment insurance. When the economy is in an expansionary phase, the government has to pay fewer claims of unemployment. When the economy is contracting, then the government has to pay more unemployment claims. This is an automatic stabilizer because it helps moderate the business cycle. Money is pulled out of the system by having fewer transfers when the economy is in expansion. Conversely, recessions are not as bad because unemployment benefits are spend in the economy, boosting consumer expenditures (Krugman & Wells p. 388).
Figure 1 below is a representation of two different economies growing on the same track. The blue line is the economy that does not have automatic stabilizers in place. Its growth is more erratic, the peak is higher, but the trough is also deeper in comparison to the peak. The economy represented by the orange line is one that has automatic stabilizers in place, like unemployment insurance. The path is moderated so that the peaks are lower, but the trough is also not as deep as the one in the blue economy.