This isn't an easy subject. It was very fashionable 20 years ago for a couple of reasons. One was the Butterfly Effect idea: "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?". The other was the beautiful fractal patterns that come from the theory. It is based on the discovery that science is far more complicated that we thought. We normally do experiments in which we control one variable, change another and measure a third. This leads to nice straight line graphs - LINEAR results where you double one thing and the other doubles too. In the real world, this doesn't often happen. Results are NON-LINEAR. If you double one thing, the other might get stupidly big.
Actually, Chaos Theory is badly named. It predicts things. It says that there are stable states. You know that staying still is pretty stable - things tend to stay like that unless knocked. The same applies to straight line, constant speed and also to regular orbital motion. Chaos Theory suggests that things can be stable by going round and round without ever repeating themselves. The weather is a good example. It goes round and round much the same for years at a time without ever quite repeating itself. This book takes you through the discovery of this branch of Physics.