The practice in economics where policies are made to decrease government spending and/or increase taxes to attempt to lessen government budget deficit. During the fiscal crisis in New York City austerity was used to try and help decrease government debt; budget cuts and layoffs were a common part of austerity. These policies usually work to benefit businesses and corporations rather than people in a society.
For further reading: http://www.economicshelp.org/blog/6254/economics/what-is-austerity/
The Fiscal Crisis, Freeman
What is Austerity?, The Economist