I think 'Butterfly Effect' comes from one of the founders of chaos theory - Lorenz. He had designed a weather simulator which was generally considered to be a very good model of the real weather. One day it stopped (don't know if it crashed/was turned off/whatever) and he restarted it using some figures he had from the day before. However, the figures he had on his printout were rounded to a smaller number of significant digits than the ones used internally. The result was that when the system restarted it produced an initially quite similar weather pattern, which rapidly became very different to his printouts from before the stoppage.
Rather than assuming (as I'm sure many of us would have done) that there was some problem with his system, he decided that the weather must really behave that way - and the difference between internal numbers and his printouts - at the n'th significant digit - gets magnified to a massive change.
Or in short/soundbite mode - the difference of a butterfly flapping its wings on one side of the world might result in a hurricane on the other.
Sadly this seems to have been extrapolated by the popular press to something about insects being able to control the weather...
Edit: the actual quote (from his 1972 talk) is:
Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?