Equity Mutual Funds buy stocks while Debt funds buy debt fund securities like bonds for their portfolio. Securities like bonds aare issued by corporates such as power utilities, banks, housing finance and the Government. They issue bonds with fixed interest rate to raise money from the public (investors) instead of taking a loan for new projects. Bonds are a promise to pay periodic fixed interest to investors who buy them.
When investors buy bonds with a maturity of a few years, they are lending their money to the issuer (say ABC Power Ltd.) for those many years. ABC promises to pay periodic interest to its investors during this time in return for the money they have invested in its bonds (=money lent to ABC). ABC is the borrower like a customer taking a home loan. The investor (your Mutual Funds investing your money) is the lender to ABC just like the bank is a lender to the home loan customer.
Debt fund invests your money in a basket of bonds and other debt fund securities.