Precious is a slime acting as a pet in Dragon Quest IX. He is the object of the quest "Our Precious Precious" in which Precious has run away.
The children will provide hints when asked. The boy says that he is shy and he will not have gone far, and he will come out if the hero wears special armor (most likely pertaining to the gooey gear, slime earrings, and the slood). Then he says you need to fight him in battle.
The girl says he is a slime, by saying he is blue, wobbly, a pointy head, and wears a red collar.
You find Precious at the place before you enter the place near the spirit train. Once you have equipped ONLY the slime based items, you go and fight slimes, then, after a battle of a slime, the game may say that the slime has a red collar on, and walks toward you. Then you talk to the children, and complete the quest after you then talk to their mother.