I find the entire concept to be unavoidably confusing. In accounting, to "balance the books" means to complete the process of double-entry bookkeeping. Once the books are balanced you can then determine whether you made a profit or a loss.

The political term "balance the budget" seems to be a corruption of the accounting term, and it means just for the state to break even. It seems likely to me that the coiner of this term had some misconception about double-entry bookkeeping - such as that you break even iff your books are balanced