Linear systems behave nicely - whenever you slightly increase the input, the output also increases only by a small amount. Thus linear systems are quite easy to predict. You can make small errors in measurements of your inputs, which will have almost no impact on the accuracy of your prediction.
Nonlinear systems are different in this regard - even small difference in the input can lead to divergent outputs. In other words the differences between the systems trajectories, or alternatively differences between your prediction and the actual behavior of the system, won't be noticeable at first, but with time those small differences will get amplified. Typical example being weather, where tomorrows forecast are likely to be more reliable than 7-day forecast.
More nonlinear systems, dynamical chaos and chaos theory in the following video by Seeker. We invite you to watch it.