The goal of controlled fusion research is to create a miniature star in the laboratory, and to try and harness the energy that is released.
Nuclear fusion occurs all the time in the interior regions of stars.
In the process lighter nuclei fuse together to form heavier nuclei and release tremendous amounts of energy, thus heating the interior of the star. As you might imagine, matter as we know is ceases to exist at such high temperatures. Other places where plasmas exist include the sun, inside flourescent and neon light bulbs, ion rocket engines, and plasma processing devices used to etch semiconductor materials. If you are interested in learning more about this concept you may jump to the National Ignition Facility Homepage for a more detailed discussion. The approach advocated by the LCT research program has grown out of the magnetically confined approach.