Before trying to figure out what automotic stabilizers are, it is necessary to first understand the business cycle.
Business cycle recap: An economy experiences fluctuations. They go through periods of expansions and recessions. Period of expansions are characterised by: high aggregate (total) demand, high growth, low unemployment and rising prices. The opposite happens in recessions. Periods of recessions are characterized by: low aggregate demand, low or stagnant growth, high unemployment, and declining prices.
The role of automatic stabilizers is to even out the those economic fluctuations so that they are less severe and volatile. In effect they reduces these short term fluctuations. This makes the economy more stable.
There main automatic stabilisers are proggerssive income tax and unemployment benefits.
Progressive Income Tax: By definition, progressive income taxation is the taxing mechanism in which the taxing authority charges more taxes as the income of the taxpayer increases. During periods of expansions, people's incomes increases. Therefore, the tax they have to pay is higher than it would have otherwise been. This means that their disposable income is less than what ot would have been without a tax. With less disposable income, the increase in aggregate demand would be less than it would have been without the tax. Therefore, the expansions becomes smaller. Thus, progressive taxations has resulted in a smaller fluctuation in the economy.
The opposite happens in recessions: taxations become relatively less - disposable incomes become relatively more - aggregate demand becomes relatively more - the size of the recessions is reduced.
Unemployment benefits:
The other automatic stabilizer is unemployment benefits. These are payments made by the government to people who are unemployed, meaning that they are actively seeking work but cannot find a job. During recessions, unemployment is high, meaning that a lot of unemployment benefits needs to be paid. With unemployment benefits people are able to afford more things that they would otherwise do without it. Therefore aggregate demand increases, and that, by definition, reduces the size of the recessions.
The oppositie happens in expansions. More people are employed > less unemployment benefits are paid > aggregare demand is relatively less > the size of the expansion is relatively less.