In the Chaos Theory, the Butterfly Effect is a sensitive dependency on conditions in which even the slightest, seemingly non-related event can have a HUGE difference on the outcome of another.
The name of this theory, credited to have been named by Edward Lorenz, comes from the example of the possibility of a hurricane starting based on whether or not some faraway butterfly flaps its wings.
The Chaos Theory studies systems that are highly susceptible to change such as in the Butterfly Effect. Henri Poincaré described this in 1890 and proposed that this problem could be common in meteorology, for example.
Edward Lorenz was re-running a weather predicting machine in 1961 when he realized that even a small inaccuracy in the thousandth of a decimal place in the number he entered could have a drastic effect on the weather. He later coined the phrase "Butterfly Effect" and his theories supported Poincaré's proposals.
Essentially, it means that everything we do is important. A butterfly flapping its wings does not cause a tornado, or a hurricane, but can start a chain of events that eventually does. So by this notion, its important to think of the consequences of our actions and how anything we do, no matter how small, can have a big effect on the rest of the world, for better or worse.