In banking and accountancy, the outstanding balance is the amount of money owed, (or due), that remains in a deposit account.
"Balancing the books" refers to the primary Balance sheet equation of A=L+OE, or Assets=Liabilities plus Owner's Equity. The first "balancing" of books, or of the balance sheet financial statement in accounting is to check iterations (test balances) to be sure the equation above applies, and where Assets and Liabilities are unequal, to equalize them by debiting or crediting Owner's Equity (i.e. if assets exceed liabilities, equity is increased, if liabilities exceed assets, equity is decreased, both in the amount needed to balance the equation).
In addition to the balance sheet, the other primary financial statement (the P&L or Profit and Loss Statement) also is balanced against the balance sheet, generally by use of a "plug" such as imputed interest.