Federalism is the political idea that some policy-making powers are better performed at different levels. This is most expressed in countries like the United States, where each state (and often each county or government) is given a lot of lee-way in how to run its own affairs, or Spain where each separate cultural region is given similar power. The United Kingdom has seemingly hopped on the federal bandwagon, to some extent, with the creation of separate parliaments for Scotland and Wales.
Within the US, there is a lot of rhetorical support for federalism from all sides of the political spectrum, but actual support for the principle seem to depend on whether one agrees with the national government's stance on a given issue: liberals want federalism on marriage and drug use, conservatives want it on religious indoctrination and abortion laws.
There are many services and bureaucracies that could only function effectively at the federal level, such as the FAA. Unless you'd like having poorly maintained planes from Texas crashing every week.