A part of the chaos theory that states that one small change in a situation(expieramental noise) can drastically change the outcome of an event. Butterfly comes from the example of the flap of a butterfly's wing altering the atmosphere around it causing(or preventing) a major event somewhere else.
Also a movie with that Ashton Cootchie
Example 1: The Butterfly effect is a cool mathematical theory.
Example 2: The Butterfly effect was supposedly based on Chaos Theroy although there is no correlation whatsoever.