Answer
The adjusted cash book balance is the cash book balance after updating it for items appearing on the bank statement but not yet recorded (charges, interest, direct debits, dishonoured cheques) and correcting any errors. This adjusted balance is the figure that the reconciliation ties to the bank statement (after timing differences) and is used in the accounts.
Real-world example After posting bank charges and a direct debit, the adjusted cash book balance is the true bank figure for the accounts.