Interest is paid on an investment. For example, ordinarily, I can deposit my money with a bank and they will put that money to work and they'll pay me "interest" for the time that they have my money. They're keeping my money safe, but they're also profiting from it being with them and not with me. So they pay me, proportional to the current "interest rate" or "rate of interest". That rate is usually greater than 0. However, if the interest rate falls to below 0 then the bank doesn't pay me interest. Rather, I have to pay the bank interest for keeping my money safe. That's what it means when the interest rate (or interest rates) go negative.

I have a Swiss student who says that the Swiss banks are so rich that YOU have to PAY them to put your money in their banks. He told me about the negative interest rates there. I'd never even heard of such a thing before! Over here the interest rates are low, but at least they are not negative.

I have never heard of it. In the USA the interest rate is so low, they are just printing money, that has no value, which in turn devalues the Dollar. That could be considered a negative interest. Last week during the Superbowl the bets placed on The Patriots were negative interest rate. Meaning you had to place a bet of $115 to win $100.