Please explain this to me like I am 5 years old.
I'm not sure how redoing it will save us money in the long run. I can definitely see how it would save us money in the short run, but like I said, please explain like i am 5. No sarcasm here, definitely like I am 5yo.
I will try to help a bit but I agree with pp that we can't explain how it will save you money because, ultimately, it might not. Depending on all the figures (how much you've paid, how much you still owe, current rate of interest, new rate of interest) - it might not save you money overall.
I will tell you that even though it might look like it will save you money in the short run, don't forget about closing costs/mortgage tax. Basically for refinancing you will have 'fees' that need to be paid now to get it all done. So even though your monthy out of pocket might go down, you will have to have some cash to outlay to get it done - overall not saving you money right now but costing money right now.
We refinanced a couple months ago. We were able to go from a 30 year to a 10 year mortgage - that helps to save a lot of money if you are able to reduce the # of years. But we had to pay approx. $1800 upfront for all the associated fees for the closing/refinancing.
Generally speaking some rules of thumb are that if you are able to go down at least 2 percentage points it 'might' make sense to do it. For example, if you are paying 6.75% interest right now and can go down to at least 4.75%. Also, general rule of thumb if you don't plan to be in this current home for at least another 5 years then it is often considered a bad idea to refinance. Of course, not in every case - but generally speaking.
If I was explaining it to my 8 year old I would say 'When you borrow money, you have to pay back extra money since they let you borrow it. This is the interest. By having a lower interest amount you're paying less to the company who let you borrow it. When you refinance, you want to have a lower interest rate so that you can pay the company less and keep more in your own pocket.'
If you go to a local credit union with a copy of your current mortgage bill, I bet someone would be able to walk you through it step by step.