Variable interest rate, also called floating rate, is the rate that varies with market interest rate. As market interest rate increases, variable interest rate also increases and vice versa. Often the loan provided by bank has fixed interest rate but sometimes bank may provide loan by charging variable interest on it which fluctuates over time. Although it has higher interest rate risk, borrowers may take a advantage of lower interest rate as it gradually decreases during it's maturity.
Let's see this example to be more clear: