Mystery Discs (also called Disc Stones or Saucer Stones) are flat, spherical tablets that contain a monster's genetic makeup inside. These were said to be created by Colona and entrusted to the Tochikans as a way to help them and give them companionship.
As you can imagine, there were originally not that many mystery discs. Each one contained the DNA of a basic breed of monster, but as monsters became more commonplace, their genetic information was combined to create many more types. Later, the Pendant scientists created their own man-made versions of the saucer stones, called tablets.
In most Monster Rancher videogames, these stones are represented by the CD's the player uses. Each CD contains information that helps you unlock a specific monster breed.