Can someone explain the Butterfly Effect to me?

I heard a speaker talk about it, relating it to Chaos Theory. She mentioned the difference of rounding numbers to the 3rd decimal, and then to the 6th decimal, as being huge. Then she went on to talk about a butterfly flapping its wings in Asia causing a hurricane in Florida. I was a little confused about the relationship of these 2 situations, but she did seem to relate them. Was it that if a meteorologist rounds a number to the 3rd decimal, instead of the 6th, he or she will create such disarray that it would be like a butterfly flapping its wings in Asia causing a hurricane in Florida?

Does anyone know?

It's covered in James Gleick's book on chaos. Have a look here and here. Basically, small changes can have big effects, if you let the simulation run long enough.

There's also a somewhat lame movie by that name that plays with the idea that one can never do just one thing; every action has multiple consequences.

That reminds me of those back to the future types of movies. It is amazing, when you think about it, how every little thing you do can have a big consequence. For example, if you miss your flight, and then the original plane crashes, fate has saved your life.