This is just my personal opinion, but I believe it might be some form of energy entity.
The Ten Wise Men use the Sphere to alter the orbit of Expel so that it will collide with Energy Nede. It was sealed in Eternal Space billions years ago along with the Ten Wise Men until they escape and end back in normal space, only to land on Expel. The Ten Wise Men use Expel as their vessel simply because it has the closest orbit to Energy Nede; their intended destination.
Upon arriving on Expel in S.D. 366, the Quadratic Sphere starts to emit heavy radiation that exerts a strong negative impact on the lifeforms of all continents. Docile animals become feral and mutate into ferocious monsters that immediately begin to attack people. The kingdom of Ell had been completely destroyed by the monsters created by Quadratic Sphere, while the Kingdom of Lacuer has been busy preparing for a war against the monster army which had destroyed said kingdom. Residents of planet Expel firmly believe that the 'Hero of Light' will come to their rescue, though it is nothing but a fairy tale passed down from their clergy.
When the party confront the Ten Wise Men for the first time of the game on top of Eluria tower, it is revealed that Rena's pendent, the quadratic key, has amplified the effect of the Quadratic Sphere. This interaction has resulted in Expel moving towards Energy Nede hundreds of years faster than the Ten Wise Men have originally planned. The party attempt to save Expel, but they are unable to do so. In the end, the party are teleported to Energy Nede together with the Ten Wise Men. Expel is violently destroyed after colliding with Energy Nede's powerful energy field in open space.