If the country experiences inflation, the Treasury marks up the value of the bond. If the country experiences deflation, it marks it down. Treasury pays interest on the adjusted value of the bond, not its face value. And it pays back the adjusted value of the bond, rather than its original face value, when it matures.
So, let's say that you bought a $100 five-year bond with a 0.5 percent coupon at its face value. For a normal bond, Treasury would give you $2.50 in interest payments, plus your $100 back. But let's say that inflation increased 1 percent per year over the life of your bond. With a TIPS bond, Treasury would compensate you for that change. It would mark up the bond from $100, to $101, to $102.01, to $103.03, to $104.06. Your interest payments would total about $2.56 over five years. And you would get $104.06 back when you cashed in. With a normal bond, you would have lost money in real terms. With a TIPS bond, you would have come out a bit ahead.
Investors at Monday's auction paid $105.50 for a $100 five-year bond with a 0.5 percent coupon. All things being equal, the investors overpaid—hence the negative yield. But that just means that they expect inflation to be positive for the next five years. Crunching the numbers, annual inflation for the next five years needs to be somewhere north of about 1.55 percent for the investors to break even. Any more inflation than that, and they make money.
So why do so many investors think that inflation might head upward? Because next week, the Federal Reserve is expected to announce a new round of quantitative easing—printing money, and possibly stoking inflation. Of course, not everyone believes the Fed's policy will have that effect. In that case, these negative-yield bonds will be true to their name.