The butterfly effect, used to describe many chaotic phenomena, was first described as such in reference to weather: that the beating of a butterfly's wings in Brazil might set off a tornado in Texas months later1. Chaos theory posits that complex systems such as the weather, or the stock market, are difficult to predict due to their sensitivity to small changes. The cumulative effect of these small changes, and their timing, makes it very difficult or impossible to predict future conditions with a high degree of certainty.
1Edward Lorenz, in a paper in 1963 given to the New York Academy of Sciences, said: "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings would be enough to alter the course of the weather forever." Later speeches and papers by Lorenz used the more poetic butterfly.
The expression butterfly effect itself seems to be based on the sci-fi short history A Sound of Thunder, written by Ray Bradbury in 1952. In the history, a time traveller accidentaly steps on a butterfly, changing his entire future.