OK, this probably is going to sound pretty stupid to some of you, but hopefully somebody can help me out here.

I am applying for a relatively small loan with my bank, using my home as security. The loan officer seems to assume way too much regarding my understanding of the terms, and has thus far not been very helpful in explaining things to me.

She says my interest rate will be 6.75% fixed, and that it will be a 35 month balloon with a 84 month payment amortization. The loan amount is $21,417.00, and the payments $321 per month.

I've heard that balloon payments mean I'm going to have a really big payment, presumably at the end of the 35 months, but the loan officer says that the bank will continue the loan at that time at the current market rate.

Can somebody explain this in language that I might understand? My loan officer seems to think that repeating her statements constitutes explaining same, but I'm worried about making a mistake that's going to cost me money I can't afford here, and would appreciate some input from someone who isn't being paid to get me to sign a contract....

The reason the bank will offer you an 84 months payment amortization is because you probably cannot afford, based on the bank guidelines, the payment if the amortize the loan for 35 months.
In this case, you will not be making a significant reduction to the principle of the loan, and at the end of 35 months you will have a final balloon payment that it most likely is going to be large. At that time you will have to, either pay that off or refinance it. The bank is telling you now that they will do that, however, they cannot guaranty it. It is a decision you need to make.

21K is not a small loan. What is this loan for? Is it worth possibly losing your home? I am not a fan of using the roof over your head as collateral. Sounds like you will be paying a lot in interest. I also would not count on a refi. There are a lot of variables that go into that and it may not be in your best interest. Also, you may not qualify and/or lenders may not be interested in refi for you. That is one thing that got a lot of people in bad and losing their homes. You might want to check out a payment calculator.

Maybe a few of these will help.

Homes and Communities - U.S. Department of Housing and Urban Development (HUD)
Compare Mortgage Rates | CD Rates | Credit Cards Home Equity Loans Mortgages Best Rate Calculator Bankrate.com
Financial Calculators from Dinkytown.net

i've never heard of a balloon loan.