How much your payment goes down when you refinance depends on several factors, including the amount of your mortgage, your current interest rate, the length of your remaining mortgage term, and the interest rate and terms of your new mortgage.
For example, if you have a $300,000 mortgage at a 4% interest rate with a 25-year amortization period, your monthly payment would be $1,581. If you were able to refinance to a 3% interest rate, your monthly payment would decrease to $1,410, saving you $171 per month.