On a debt collection agency's letter, what does "balance" refer to?

The balance is the amount due.

Without more info to go on (such as a screenshot of the relevant portion of the statement or what country you're in), I will run with the answer that "balance" is the amount the collection agency is attempting to collect from you, including any and all fees the agency may have added.

One important idea to keep in mind is that depending on how old the debt is, the amount involved, and the importance to the agency to collect it, you may be able to negotiate a settlement for less than the full amount. This isn't always possible, but sometimes you get lucky, and it doesn't hurt to try.

Collection agencies work in several ways. Some will actually buy the outstanding debt from the original creditor for some percentage of the debt's face value and then take their chances on whether they collect anything at all, while others work on behalf of the creditor and earn some percentage of what they manage to recover. In the latter case, your chance of negotiating a reduced amount is better, because the agency is being evaluated by the creditor on how quickly and efficiently they collect debts. An agency that is slower or less effective than another is less likely to continue earning the creditor's business.

I hope this helps.

Good luck!