refinance

What is refinance, please?

I bought my house in 2004. It is 4.5% interest for 10 years. Now I have about $80000(interests included) almost 4 years left.

I talked with a mortgage consultant at Wachovia bank. She said she could give me 4% for another 10 years. This way, my monthly payment will be half of my current monthly payment.

She said I could not save much since I paid over 5 years and paid most of my interest.

I am lost. If no cost to me, no prepayment penalty, I can have 4% rate in stead of 4.5%, why can't I save money besides the tax part?

Would anyone help me out?

I greatly appreciate it.