The best supercomputers fill rooms, cost millions, and are thousands of times faster than your computer at home. They are usually used for complex scientific problems involving lots of maths. They are used to predict the weather, model brains, or help predict the result of a nuclear explosion, for example.
Some are used to test the strength of encryption (computer security) methods. They have been used to model the spread of swine flu, to predict climate change, and even to understand the Big Bang at the beginning of the Universe. But technology moves quickly. A top-end desktop computer today calculates at the same speed as a supercomputer 10 years ago.