Supply and demand determine the inflation rate.
When supply grows, prices rise because each individual unit of currency is less valuable.
More bank loans = more money in supply (fractional-reserve-banking-is-how-money-is-printed).
Therefore, lower interest rates = higher inflation, because there is a larger supply of money due to higher demand for low-interest rate loans.
Federal Reserve and money supply
The Federal Reserve buys and sells government bonds and bills it has issued in order to increase and decrease money supply and thus the short-term interest rate. The money supply dictates how much excess reserves there are and in turn the activity of Federal Funds.