To refinance a loan is to start the terms over again, usually with a lower interest rate. If you buy a house with a mortgage at a high interest rate, you may be able to refinance later and pay less each month.
When you take out a loan from a bank, you always have to pay interest — you agree to pay the money back, plus a certain monthly or yearly percentage of it. If this percentage is high, or the monthly payment is too much, you can sometimes refinance the loan and get new terms that are better. Finance was originally an Old French word meaning "payment" or "settlement of a debt."