Devolution is a term that describes the "return" of powers from the federal government to the states. It presumes that the central government has taken on a role relative to the states that is too expansive and wasteful. Devolution was a central feature of President Ronald Reagan's campaign in 1980. Reagan continued the use of "block grants" given to each state, allowing them to use federal monies in ways they saw fit. This had the effect of placing more of a spending burden on the states. The Reagan Administration also relaxed environmental, financial, and other regulations, allowing states to enact regulations of their own.
The so-called "Republican Revolution" that followed the midterm elections of 1994 contributed to devolution in one important way—welfare reform. Generally, they also supported "block grants," part of a program known as Temporary Assistance to Needy Families (TANF) that was actually signed into law by President Bill Clinton, were intended to give states more flexibility in getting people off of welfare rolls, thus minimizing federal aid in a program many conservatives had long disliked.
In short, these programs, which really began in the Nixon era, represented an attempt to "devolve" decision-making powers and fiscal responsibilities, to the states. This represented a departure from previous policies and throughout the period was known as "New Federalism" because it heralded a new relationship between the states and the federal government.