A firm letter is a letter in which you express your opinion clearly and strongly (while still being polite).

An example of language that is polite, but NOT firm--because it doesn't say what the speaker wants the store to do or what the speaker intends to do, and seems to leave open possibilities: "I'm afraid the cell phone I bought turned out to have a cracked case when I opened the package. I'm really disappointed that you wouldn't exchange it for me." An example of language that is polite, but firm: "Your customer service desk refused to exchange the defective phone I bought. I think it would be faster and easier for both of us if you let me exchange it for another one. It will save me the time of calling my credit card company to dispute the bill." Another example of firm language. "Thank very much for the time you've spent with me on this; it was every helpful. Nevertheless, I have made my decision and it is final."