Interest is paid by a bank when money is deposited because the bank uses that money to make loans. The bank then charges the borrower a little more for that same money so it can make a profit for its service.
When interest rates are high, fewer people and businesses can afford to borrow, so this usually slows the economy down. However, more people will save (if they can) because they receive more on their savings rate.
When the central banks set interest rates, such as the U.S. Fed Funds rate, it is the amount they charge other banks to borrow money. This is a critical interest rate, in that it affects the entire supply of money, and hence the health of the economy.

