An automatic stabilizer is a non-discretionary item in a government budget which kicks in automatically when economic activity decreases.
Unemployment benefits are an example of automatic stabilizers. As economic activity decreases & workers are laid off, the automatic stabilizers kick in to provide a floor of support.
This is a critical concept when talking about Government deficits, because it means that the deficits themselves are outside of the direct control of the budget process. We could say the deficit result is endogenously determined, that is, it is determined by events in the private sector of the economy.
Targeting a desired deficit outcome (such as a balanced budget) becomes impossible because if private sector activity decreases, as people are laid off the automatic stabilizers will kick in and throw the desired deficit result off track.