When you park your money in a fixed bank deposit (FD), the bank promises to pay fixed interest in return. Here you lent money to the bank, and the bank is a borrower of your money, it owes you a fixed periodic interest. Debt mutual funds invest in debt securities such as government bonds, corporate bonds, money market securities. Bonds are issued by corporations such as power companies, banks, household finance companies and the government. These bond issuers promise to pay their investors (those who buy their bonds), periodic interest in exchange for their money invested in the bonds.
Bond issuers are like the bank (borrower) in our FD example, borrowing money from investors and promising to pay periodic interest. While you are the investor in an FD bank, the debt funds are the investors in these bonds. Just like earning interest from an FD, debt funds earn periodic interest from their bond portfolio. Unlike FD guaranteed interest, periodic interest payments to fixed-income debt funds from these bonds can be fixed or variable without any collateral. When they sell bonds from their portfolio, get their capital back. When you invest in a fixed income mutual fund, you invest indirectly in its bond portfolio, spreading risk among different bond issuers. You benefit from this risk diversification.