Generally part of a story about accepting things as they are, this is the sword held over the heads of repeat offenders of Hitler's Time Travel Exemption Act, those who insist on changing the past. The resultant world can range from a dark Alternate Universe to a full-blown Mirror Universe. Heroes can usually Set Right What Once Went Wrong, by undoing the original change with a bit of Rubber-Band History. Curiously, these changes are never positive, suggesting in all cases shit happens for a reason.
Intuition dictates that big changes have big causes, and small causes equal small changes. This trope is named partly for the Butterfly Effect , an observation made in meteorology. In the large-scale computer simulation of weather systems, a minuscule change in temperature or the wind's direction (about the beat of a butterfly's wings) will drastically alter the weather (sunshine instead of hurricanes) simulated at a later point. Even if the models used work, it is impossible to achieve sufficient accuracy when entering the data. Thus computer-assisted long-term weather forecasting is considered a joke even by meteorologists.
The Of Doom is appended because the image of a single frail, pretty, delicate-as-a-sheet-of-glass butterfly causing the world to turn itself inside out is amusing. In Real Life, the butterfly does not actually change the expected mix of storms; a flap of the wing may cause hurricanes, hailstorms, typhoons, tornados, blizzards, but it would be equally likely to prevent those storms. Probably, it causes about an equal number of both changes, but the Butterfly Effect makes it impossible to tell which ones. That being no fun at all, writers tend to opt for the Doom scenario.
This alone may be a bad reason to argue for a universal butterfly effect. Edward Lorenz's Chaos Theory is based on the idea that an unstable system is unpredictable and a small change can have a large impact in the long term. Not all systems are unstable, though. This is why there is no scientific reason to claim that the whole universal system is unstable as well. Further, "Chaotic" does not mean entirely random. Systems defined as "Chaotic" may be unpredictable, but they still are deterministic. That is to say, that if you knew the exact value of every parameter that influences the state (the weather) at a given moment, you would be able to predict the state of the next moment (forecast the weather). Precise knowledge of every parameter, however, is a difficult assumption to fufill and is physically impossible
with current technology and knowledge in the context of weather in nature due to Heisenberg's Uncertainty Principle.
The butterfly effect also refers to Ray Bradbury's seminal time travel story "A Sound of Thunder", which centered on the disastrous consequences of a butterfly's death. By marvelous coincidence, the story was written ten years before Lorenz began pondering the inaccuracies of his forecasting computer.
In theoretical discussions of Time Travel, this phenomenon is sometimes referred to as "Avalanche Time", evoking an image of cascading changes that race forward through the timeline exponentially, obliterating everything familiar to the time traveler who set it off.
There is a philosophical history regarding this trope as well. Leibniz theorized that God made this the best of all possible realities. Ergo, any change would be tampering with perfection. Therefore in Western Media, the Butterfly Of Doom is God being sort of a dick. (Leibniz's philosophy was parodied in Voltaire's Candide, with Doctor Pangloss who, no matter what horrendous atrocity he beheld, would exclaim that every thing was for the best in the best of all possible worlds).
The most common aversion of this trope is based on the idea that large-scale historical processes happen for large-scale reasons. The Butterfly of Doom may alter the course of a hurricane, but it can't stop winter from changing into spring.