What is Interest?:
Interest, as defined by economists, is the income earned by the lending of a sum of money. Often the amount of money earned is given as a percentage as the sum of money lent - this percentage is known as the interest rate. More formally, the Glossary of Economics Terms defines the interest rate as "the yearly price charged by a lender to a borrower in order for the borrower to obtain a loan. This is usually expressed as a percentage of the total amount loaned."
Interest Types and Types of Interest Rates:
Not all types of loans earn the same rate of interest. Ceteris paribus (all else being equal), loans of longer duration and loans with more risk (that is, loans that are less likely to be paid off) are associated with higher interest rates. The article What's the Difference Between all the Interest Rates in the Newspaper? discusses the different variety of interest rates.
What Determines the Interest Rate?:
We can think of the interest rate as being a price - the price to borrow a sum of money for a year. Like almost all other prices in our economy, it is determined by the twin forces of supply and demand. Here supply refers to the supply of loanable funds in an economy, and demand is the demand for loans. Central banks, such as the Federal Reserve and the Bank of Canada can influence the supply of loanable funds in a country by increasing or decreasing the supply of money. To learn more about the money supply see: Why does money have value? and Why Don't Prices Decline During A Recession?
Interest Rates That Are Adjusted for Inflation:
When determining whether or not to loan money, one needs to consider the fact that prices go up over time - what costs $10 today may cost $11 tomorrow. If you loan at a 5% interest rate, but prices rise 10% you will have less purchasing power by making the loan. This phenomenon is discussed in Calculating and Understanding Real Interest Rates.
Interest Rates - How Low Can They Go?:
In all likelyhood we will never see a negative nominal (non-inflation adjusted) rate of interest, though in 2009 the idea of negative interest rates became popular as a possible way to stimulate the economy - see Why Not Negative Interest Rates?. These would be difficult to implement in practice. Even an interest rate of exactly zero would cause problems, as discussed in the article What Happens if Interest Rates Go To Zero?