A 1099 from a bank or other financial institution usually lists the amount of interest your accounts have earned this year (when you have complicated enough finances, you'll also get similar forms listing how much interest you've paid on your mortgage or student loans). When you file your 1040 (whichever version) there will be a line to list how much interest income you've earned this year. It will be added to your income and you'll pay taxes on it. On the 1040EZ, which I'm guessing you use if you haven't had 1099s before, you report this on line 2.
Last year I made a mistake on my taxes, and the IRS owed me $1000, which they couldn't figure out for 3 months. They paid me interest on that $1000 - and then sent me a 1099 so I can pay taxes this year on that $25-$30.