Chaos theory is a mathematical field aimed at analyzing the behavior of dynamical systems that are highly sensitive to initial conditions. A deterministic system can be chaotic in such a sense. Chaotic behavior places a limit on the length of time for which predictions can be made.
Applications include meteorology, physics, engineering, economics, biology, and philosophy. In astrophysics, it can apply to orbital mechanics when more than two bodies are involved.
For the purpose of the theory, an example of a phenomenon considered non-chaotic is the shooting of a cannon, where a slight change in aim or projectile speed causes a slight change in the path of the projectile, and you can "zero in" on a target through repeated shots, making adjustments. In contrast, a pin-ball machine is considered chaotic since a very slight change in setting the ball in motion can cause the ball's path to change dramatically after hitting a few of the obstacles, and attempting to use fine adjustments to produce predictable changes in the results is essentially useless.