UPDATE: A few people, plus at least two sentient robots and a self-aware Jovian gas cloud, have written in to ask just what the hell is going on in that glass. I would have thought the robots, with their advanced brains, would have figured it out, but here goes anyway.
What you're looking at is known as an oscillating reaction. If done properly, the reaction will continue to occur for several minutes, until the solution settles at dark blue. This particular one is called the Briggs-Rauscher reaction, after the two high-school science teachers who came up with it in 1973. The reaction occurs when three different solutions are mixed together. I would go into greater depth, but I don't understand the chemistry behind it. For detailed instructions on how to create this reaction, along with an explanation for its niftiness, can be found here. Remember that chloride ions suppress the oscillating reaction, so make sure to pick up all the chloride ions you've got lying around and put them in a bag somewhere. And use distilled water.
No matter what you think of this process, it's definitely the coolest possible way to create a jar of deep blue liquid.