Elliott Wave Theory is a method of analysing markets based on patterns of past price action and how these patterns relate to a simple master plan. The master plan is that there is an impulse wave consisting of 5 parts, followed by a corrective wave, usually of 3 parts but which can get somewhat complex.
The master plan has a number of rules in particular relating to the relationships between the various waves and uses Fibonacci numbers including the "Golden" ratio of 61.8%.
Elliott is a very optimistic theory as down moves are always corrective and new impulse moves always go to new highs eventually!