Equity Funds are open to market risk i.e. there is a possibility that the price of the stocks in which the fund has invested may decrease. Of course, the prices may also go up, making it possible for the fund to earn superior returns
Debts Funds are open to two main types of risks - Credit Risk and Interest Rate Risk. Credit Risk refers to the possibility that the company which has issued the bond or debenture in which the fund has invested may default on interest or on principal payments. Debt fund managers take care of this by investing in debt securities which have good credit rating.
Interest Rate Risk refers to the possibility that the price of the bond in which the fund has invested may go down because of an increase in the interest rates in the economy. In general, it is useful to remember that this is a "see-saw" relationship - bond prices (and therefore the NAV) go up when interest rates drop and vice versa.