The fed funds rate -- short for federal funds rate -- is the interest rate at which banks lend to each other overnight. As such, it is a market interest rate. But the Fed sets a target for the fed funds rate, and keeps the rate on target via open market operations. Unless otherwise specified, references to the fed funds rate are actually to the fed funds rate target (on any given day, the actual rate may differ from the target rate slightly).
The fed funds rate target is set by the Federal Open Market Committee, the Fed's monetary policy committee. As the U.S. short-term benchmark, it influences market interest rates throughout the world.