Why does the US Federal Reserve raise interest rates?

One of the primary roles of the US Federal Reserve is to control the supply of money within the economy.  During times when the economy is doing incredibly well, a.k.a. running hot or facing inflation (rise of prices of goods and services), the Federal Reserve will need to reduce the supply of money by increasing the cost of borrowing.  

The primary lever to increase the cost of borrowing is by increasing the Federal Funds rate (the rate for banks to borrow and lend their excess reserves to meet liquidity requirements). Increasing the Federal Funds rate results in more expensive borrowing costs, which can reduce demand among banks to borrow money.  Less money is borrowed to help fund the economy resulting in a reduction in purchasing power and the money supply.  This will slow down the pace of economic growth and help ease inflation.