Acting alone, gravity would cause stars to collapse completely, but as long as energy is produced at their centers by nuclear fusion (the joining of atomic nuclei to form new elements, as in a hydrogen bomb), the star is heated and puffed up.
This project, a collaboration between America, Russia, Japan and Europe, is intended to create sustained nuclear fusion by squeezing gases so hard that their atomic nuclei fuse together and give off more energy than was needed to squeeze them.