Elliot Waves are named after Ralph Nelson Elliot, the person who discovered the Elliot Wave principle. This principle reflects the psychology of investors, and can be seen in the form of price changes and movements in the financial market. In short, when investors are optimistic, they will drive the price up; alternatively, if they are pessimistic, they will drive the price down.
When you study the historic charts of any financial market, you'll see that they unfold and move in waves. Elliot Waves are an exercise in predicting where the market will go, based on probability. Those who use Elliot Waves (Elliotticians) are traders who identify the market structure and who tries to anticipate where the market will go next. By studying and understanding the wave patterns, Elliotticians are able to know what the market will and won't do next. It's all about identifying the highest probable move with the least amount of risk.
The Elliot Wave principle identifies patterns in market prices. To use the principle effectively, you need to analyze and study chart waves. The patterns consist of two types of waves: 'impulsive' and 'corrective.' Five subwaves make up an impulsive wave. It progresses in the same direction as the next larger size trend. A corrective wave consists of three subwaves, and it progresses against the next larger size trend. 
The first task of applying the Elliot Wave principle is to study the charts and identify the five-wave structures as well as the three-wave structures. Once they've been identified, you can predict where the market is headed. The key word is 'predict.' It's important to note that the Elliot Wave principle is based on probability, not certainty.
Many traders use the Elliot Wave Principle in conjunction with the Fibonacci ratios. Together, they are extremely powerful tools and can tremendously reduce the risk that trading and investing can bring. The Elliot Wave Principle can help you identify when to enter or exit the market as well as what direction the market will likely take. Many software programs, such as Mt4, include indicators and strategies for using the Elliot Wave Principle. It takes time to learn, but is well worth it to reduce the amount of risk on each trade.