This is loan the government takes to pay for its expenses. The interest rate the government pays on these securities is determined by the FED, and it is one powerful weapon to regulate an economy. The government is the lowest risk debtor in a country, so anybody who wants borrow must pay more than what the government does. If the FED raises the rate, the rest of the economy follows, financing goods and investing get harder, but inflation tends to recede. The opposite happens when the rate is lowered.
If the government pays negative rates on its securities, the banks have to pay TO the government in order to keep money invested in securities. The effect is that the government's debt will decrease, money will flood the market, possibly resulting in a bit of inflation, but maybe kickstarting the economy (and your student loan rates might get lower, if they are not regulated and/or subsidized, which I'm not of sure since I don't live in the US).