The butterfly effect is an idea from chaos theory. A small change can sometimes make much bigger changes happen. One small incident may have a big impact on the future. The emphasis here is on the words may and can. There is no general theory which tells us what is going to happen.
Weather and events are hard to forecast, but that doesn't mean when a butterfly flaps its wings in Tokyo and Arsenal lose a match in EPL. That's just silly and impossible. However, what seem to be tiny changes in a planet's orbit can and do cause big changes to the weather: see Milankovich cycle.
Author Ray Bradbury wrote the short story "A Sound of Thunder" with this idea—time travelers make a very small change in the past that makes a large change in the present. However, remember that time travel is impossible, or at least has never been shown to be possible.
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