Zerom, monsters that eat individuals Spiria or hearts have spread around the world therefore weapons called Somas were created in order to banish all Zerom. People who possess somas manage to enter someone Spir-Maze or Heart Maze.
Kohak Hearts, who happens to be the vessel for Richea Spodune, was in search of a Soma together with her brother, Hisui Hearts. Along the way an enemy, Incarose assaults them, but they manage to escape to the sea. They are brought into a little village of Seeble, where they meet the protagonist, Shing Meteoryte. There Shing took care of both of them and introduced them to the Soma they're looking for.
During that time, Incarose makes an appearance once more; this time she manages to attack Kohak and Shing's grandfather, Zeks. Since Shing has a soma he intends to go within Kohak's Spir Maze in order to cure her. But, the plan doesn't go well and Kohak's spiria ends up shattered into pieces and placed everywhere around the world.
Anime Edition featuring cutscenes by Production I.G.
CG Movie Edition featuring CGI cutscenes created by Shirogumi Ltd.
Source: Wikipedia, "http://en.wikipedia.org/wiki/Tales_of_Hearts," available under the CC-BY-SA License.