The Federal Funds Rate (FFR) is the interest rate that banks pay to borrow federal funds. Federal law requires that banks hold a certain percentage (typically 10%) of the assets in their demand accounts (checking and savings accounts) with the Federal Reserve. These are referred to as federal funds. If a bank below its minimum federal funds reserve requirement, then it can borrow federal funds from another bank that has a surplus in its account.
The Fed does not set the FFR directly. Instead it sets a nominal or desired rate and then carries out open market operations-- the buying and selling of government or other types of securities to influence money supply. When the fed sells large amounts securities to investors, it takes the proceeds from the sale and holds them, essentially removing money from the market and increasing interest rates. When it buys large amounts of securities, it injects money into the market lowering interest rates.
Loans involving Federal Funds are typically very short in duration, overnight. These loans are often a necessary part of a banks business. Banks depend on demand accounts for a substantial portion of the funding for the loans that they make. On any given day, a bank may lose more in deposits than it takes in or the demand for its loans may temporarily outstrip the assets that it has available, requiring it to draw upon the assets in its reserve account with the Fed. Borrowing funds from another banks reserve account is an expedient way for the bank to raise capital.
When the Federal Reserve raises the FFR it discourages banks from borrowing Federal Funds and in turn lowers the amount of money that banks are able/willing to lend. This has a broader dampening effect on the economy and can lead to slower economic growth. When the Fed lowers the FFR, it has the opposite effect.