The price of a bond goes up when yields go down. For example, you purchase a 5% bond today for $100 and the very next day the same bond is being offered with a rate of 10%. Will you be able to sell you bond for the $100 you paid? No, you must compete with the 10% bonds being sold so you will have to sell your bond for less than the $100 you paid to compete with the new bonds being sold. Thus, bond prices are inversely related to bond yields.
The 20-year index you cited tracks bond prices and bond prices have gone up over the last 10 years which means bond yields have gone down.
Why have bond prices gone up? Demand. More investors are moving their savings into bonds. Why? I believe there a couple of reasons. One, US Treasuries are thought to be one of the safest investments. With the financial crisis and increased stock market volatility (see chart below) more investors are allocating more of their portfolios to safer investments.
Two, a large portion of the US population is approaching retirement (see chart below). These folks are not interested in watching their retirement portfolios potentially shrink in the stock market so they move into bonds.