Interest-rate risk is but one risk that bond funds face. The other, credit risk, involves the fund's credit quality. Credit quality simply measures the ability of an issuer to repay its debts.
Think of it this way. If your no-good brother-in-law who hasn't held a job in six years wants to borrow $50 from you, you would probably wonder if you'd ever see that $50 again. You'd be far more likely to loan money to your super-responsible kid sister who just needs a little emergency cash. The same dynamic occurs between companies and investors. Investors eagerly loan money to well-established companies that seem likely to repay their debts, but they think twice about loaning to firms without a solid track record or that have fallen on hard times.
Judgments about a firm's ability to pay its debts are encapsulated in a credit rating. Credit-rating firms, such as Moody's and Standard & Poor's, closely examine a firm's financial statements to get an idea of whether a company is closest to being a no-goodnik or a debt-paying good citizen. They then assign a letter grade to the company's debt: AAA indicates the highest credit quality and D indicates the lowest.
So if you hold a bond rated AAA, odds are very good that you'll collect all of your coupons and principal. Indeed, bonds rated AAA, AA, A, and BBB are considered investment-grade, meaning that it's pretty likely the company that issued the bonds will repay its debts. Bonds rated BB, B, CCC, CC, and C are non-investment-grade, or high-yield, bonds. That means there's a good chance that the bond issuer will renege on its obligations, or default. In fact, D, the lowest grade, is reserved for bonds that are already in default.
Of course, you probably don't want a bond that may not pay its promised coupons and principal. The main purpose in owning a bond, after all, is getting your hands on its income. So if you're bond shopping, you're not going to pick up a lower-rated bond just for the heck of it. You need some sort of incentive. That incentive comes in the form of higher yields. All other things being equal, the lower a bond's credit quality, the higher its yield. That's why you can find a high-yield bond fund with a yield of 7%-8% or more, while many investment-grade bond funds offer yields around 4%. Because investment-grade issuers are more likely to meet their obligations, investors trade higher income for greater certainty.
Credit quality affects more than just a bond's yield, though; it can also affect its value. Specifically, lower-rated bonds tend to drop in value when the economy is in recession or when investors think the economy is likely to fall into a recession. Recessions usually mean lower corporate profits and thus less money to pay bondholders. If an issuer's ability to repay its debt looks a little shaky in a healthy economy, it will be even more suspect in a recession. High-yield bond funds usually drop in value when investors are worried about the economy.