Chaos theory is a part of mathematics. It looks at certain systems that are very sensitive. A very small change may make the system behave completely differently.
Very small changes in the starting position of a chaotic system make a big difference after a while. This is why even large computers cannot tell the weather for more than a few days in the future. Even if the weather was perfectly measured, a small change or error will make the prediction completely wrong. Since even a butterfly flapping its wings can make enough wind to change weather, a chaotic system is sometimes called the "butterfly effect". No computer knows enough to tell how the small wind will change the weather.
Some systems (like weather) might appear random at first look, but chaos theory says that these kinds of systems or patterns may not be. If people pay close enough attention to what is really going on, they might notice the chaotic patterns.
The main idea of chaos theory is that a minor difference at the start of a process can make a major change in it as time progresses. Quantum chaos theory is a new idea in the study of chaos theory. It deals with quantum physics.