From the wired.com article:
Warning: This beautiful ballet of chemical reactions could make you trade your lava lamp for a magnetic stirrer.
When several clear liquids are combined, the mixture quickly changes colors — back and forth — over and over again.
In 1973, the spectacular demonstration was perfected by Thomas Briggs and Warren Rauscher, two amazing high school science teachers.
Over thirty-five years later, chemists are still trying to fully understand how it works.
What they do know: Several reactions take place at once. One of them produces iodine, which gives the amber color. Hydrogen peroxide reduces other chemicals into iodide ions. Along with normal iodine, the charged particles interact with starch to create it a blue-black color. The speeds of those transformations are constantly changing. As one overtakes the other, the color suddenly changes.
See the article here.