A system is said to have sensitive dependence on initial conditions when a small difference in input can produce a disproportionately large difference in output. A good way to see this is by performing iterations of simple mathematical procedures — feeding the result of the procedure back in repeatedly.
Here, we take a decimal fraction between 0 and 1, multiply it by 10, and drop the integer part of the result, leaving only the decimal (that is, taking the result mod 1). We then repeat the procedure on the resulting decimal fraction. The results may surprise you: two numbers that begin very close together may very quickly diverge! Try entering two numbers arbitrarily close together to see what happens.
The process is similar to folding dough: fold it in half, stretch it to its original width, and repeat; eventually, two points that started next to each other will wind up arbitrarily far apart. A good discussion of this model is provided here.