Suppose you have a 10-year bond that you bought a few years ago at a 10% interest rate. Then there was a financial crisis, the Federal Reserve went on a bond-buying spree, and now interest rates are lower. A new bond with the same amount of risk as your bond and the same amount of time left would now run about a 5% interest rate. (Insert some mathematical fiddling here to adjust for the actual time at which the bond issues interest payments, in order to come to a mathematically-equivalent bond.)
If you sold your bond today, you could sell it at a price which implies a 5% rate of return. That means more money for you!
(If this confuses you, imagine having a series of 10% off coupons, replacing them with 5% off coupons, and pocketing the difference. In fact, if you think of a bond as a coupon on future-dollars, that's a very good way to understand it.)
If the interest rate drops by 1%, then the value of the bond will change by... well, the continuous-compounding formula is
P*e^(r*t), and if we plug in 0.01 and 5 years to
e^(r*t), or 1.0512 => a 5.1% change in value. So for our bond, we see a 5.1% gain immediately. If you have a 30-year bond, a drop in the interest rate by 1% would mean a 34.9% return all at once.
(Tip: For low interest rates and short times, fudge it and just use
r * t, or
1% * 5 in our case. It'll be lower than the actual change.)
Of course, there's the question of what you'll do with the money. Consider our example when the interest rate dropped to 5%: if you just bought another bond, you'd still only get a 5% rate of return. So it's not like you're going to earn any more or less money by doing this - hence why a bond is called a fixed-income investment. You've just moved your money-making forward in time: you haven't actually generated any more of it. Likewise, if interest rates drop in the future, the face value of your bond will fall, but you'll still get the same amount of money if you hold it until maturity.
Your bond fund will own many bonds, with varying amounts of time until they mature, and will continually roll over these bonds. They will probably give you a statistic on the average maturity of their bond holdings; this average maturity will affect how much the value of the bond fund is affected by interest rate changes, the bonds' interest rate risk. You can find short-term, medium-term and long-term bond funds. Longer-term funds are more sensitive to interest rates; short-term funds are less sensitive.