Chaos theory is that branch of mathematics which studies the behavior of certain dynamical systems that may be highly sensitive to initial conditions. This sensitivity is referred to as the butterfly effect. The butterfly effect states that small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system.
Here's a fascinating look at how a little girl walking in the sand of the African desert could cause a hurricane 4000 miles away in the USA. A video from the BBC show The Science of Superstorms.