In the last few decades, physicists have become aware that even the systems studied by classical mechanics can behave in an intrinsically unpredictable manner. Although such a system may be perfectly deterministic in principle, its behavior is completely unpredictable in practice. This phenomenon was called deterministic chaos. To explain its origin, we must go back to the concept of linearity.
Linearity means basically that effects are proportional to causes.
If you hit a ball twice as hard, it will fly away twice as quickly. For example, if you are pushing a car that ran out of fuel, and want it to move twice as fast, you might either push twice as hard, or find someone else to help you push. The effect would be the same. You would not make a big mistake, though, if you would assume that the effect is proportional to your effort. Linear equations are solved easily, but non-linear ones are in general very hard or impossible to solve.