The Gaea Stones are powerful relics forged by magic that serve as vessels (and sometimes prisons) for the spirits of powerful beings, the most notable being Suzaku the legendary Phoenix lord. It is unknown exactly how many stones exist, but four are mentioned in the series to date.
After their creation, the stones were scattered across Pangaea (which was still whole at the time), and many of them were lost. Suzaku was able to put his mind into one of them (the Magic Stone) which allowed him to guide the Searchers as they looked for the pieces of his soul.
After Moo's defeat, the stone was taken to its rightful place on the altar in the Kalaragi Rainforest, where it had a wonderful effect on the people there. When the five monsters possessing the Phoenix's soul passed on to the Paradise of Monsters, his soul found a resting place in three more stones. Uniting them (like Phayne and Rio do in Monster Rancher 4) can call forth the Phoenix once more.
The fragments of a stone laced with a mysterious power are scattered across the world. Legend has it that if the pieces are collected together, the lost power of the ancients will be revived. Many a soul has searched the world for these fragments, but even those who collected the fragments failed to gain the power.
-"Ancient Stone, Parts 1-3" MR4