FAA stands for “Federal Aviation Administration” which is an operating mode of the U.S. Department of Transportation. The FAA is a governmental body of the United States with powers to regulate all aspects of civil aviation in that nation as well as over its surrounding international waters.
EASA stands for European Aviation Safety Agency which is an agency of the European Union with responsibility for civil aviation safety. It carries out certification, regulation, and standardisation, and also performs investigation and monitoring.
The FAA oversees aviation in the United States and the EASA oversees aviation in Europe.