Square-Enix--formerly just "Square" before their merger with "-Enix"--is an entertainment company based in Japan. Its name is identifiable with Final Fantasy and its offshoots (Kingdom Hearts being the most easily recognizable one for obvious reasons), but Square dabbles in much more than just video games. They do anime, too! I'd love to tell you more, but I myself only really know them for FF--not even for the RPGs that have nothing to do with FF.
Related: Video Game