The Federal Emergency Management Agency, or FEMA, is an agency of the United States Department of Homeland Security that was founded on June 19, 1978. The agency's primary purpose is to coordinate the emergency and recovery response efforts to a disaster that occurs within the United States.
FEMA, as a federal agency, is funded by the federal government as budgeted each year from available tax revenue.
Natural disasters are the first type of disaster that comes to mind when assessing FEMA's response efforts, but the organization is also concerned with response to acts of terrorism, acts of war by a foreign nation, and other manmade disasters. That being said, FEMA was heavily criticized for its response during and after Hurricane Andrew in 1992 and Hurricane Katrina in 2005.
In addition to coordinating the various local, state, and federal resources in the response efforts to a disaster, FEMA provides various resources to emergency response organizations including education and funding.
As a federal agency, FEMA employs federal employees who are coordinated and supervised by various administrators, supervisors, and directors. Their organizational chart as of November of 2016 can be found here. (https://www.fema.gov/media-library-data/1479239897769-7b1af74a3c8cf9c38…)