A subsidy is a Grant-in-aid or tax break by government (usually big government such as the Federal government) to certain businesses or to the states to help them survive or to give them a competitive advantage or to "bribe" them. Sometimes the subsidy can be direct, as in the case of cash payments to farmers, and sometimes it can be indirect, as in the case of building the transcontinental railroad.
Subsidies can also be given out by individuals or non-governmental institutions, but this is more commonly referred to as charity.
The new American Police state and militarization of local and state law enforcement is largely supported by big government subsidies ("bribes") from the Feds to the local police departments often under the guise of the War on Terror or the War on Drugs. This is called Fiscal Federalism where the flow of money is the key component to federal-state relations.