The term 'cash-register compartment' refers to the two sections of a cash register where money is stored. The first section, known as the 'tens' compartment, holds paper bills in denominations of ten or higher. The second section, known as the 'ONES' compartment, holds coins and paper bills in denominations of one or lower. Together, these two compartments provide a secure place to store money and make transactions easier for both customers and cashiers.