Interest is essentially the cost of money, expressed as a percentage of the original amount of money, or "principal". There are several types of interest, as DWarrior explains above. The history of interest is a long one; interest rates sprung up almost as soon as the currency system was formed. Almost immediately, interest got a bad name. In Greece, Solon banned the practice of forcing men who couldn't pay back their loans into slavery. Religious groups, such as Islam and Christianity, called interest usury and declared it a sin. However, wealthy merchants ignored the laws on usury, and increased their own fortunes. Eventually, interest became divided into low rates, which were acceptable, and high rates, which still was categorized as the sin of usury. In 1545, England legalized interest, but set a maximum rate that could be charge. Other countries soon followed suit.
There have been many theories about interest througout history. The Classical Theory of Interest, which was formulated by Adam Smith and David Ricardo, stated that interest was the primary component balancing savings with investment. Marx, on the other hand, believed that interest was not natural in the economy, but was instead a means the capitalists used to exploit the working classes.
The Abstinence Theory, which was formulated by Nassau Senior, presented interest as a reward for placing money in a bank instead of spending it on goods. The more a person saved, the more money they got back, and the interest rates played the primary role in whether people saved or spent. An economist named Irving Fisher used the Abstinence Theory as a foundation for his Advanced Productivity theory, in which Fisher studied how willing people were to trade present income for a potentially larger future income.
However, the most famous economic theory regarding interest was concieved by John Maynard Keynes. Keynes believed that interest rates were a reward for giving up liquidity, and that interest rates were the prime reason to invest. This model is the basis for fluctuating interest rates.
Nowadays, interest theory revolves around the problem of inflation. In the United States, it is the responsibility of each state to set the maximum rate allowed in contracts. Because of this, in 1981, the state legislatures were all able to either increase or remove the maximum interest rates to benefit corporations that lent money. In Great Britain, the government does not set a maximum cap on interest rates, but the judicial system can declare individual rates under certain circumstances to be too high.
When interest rates go too high, then businesses and consumers are unable to take out loans. This hinders the economy. The worst example of this was in 1981, where the lowest interest rates were usually 20%. Most economists disagree on what caused these exceedingly high interest rates, but all agree that some important factors were the federal budget deficits, expectations of inflation, and the policies of the Federal Reserve System. In the late 1980's, interest rates began to drop again. After September 11th, interest rates plunged to a record low. However, since the United States' economy is still in the dumpster, it can be inferred that there is a medium somewhere for interest rates at which the economy will be most efficient.