At some part of the world map, you may encounter random battles with a some sort friendly music rather then the old battle song. The creatures that appear won't attack you, instead, they want you to give them a specific jewel. If you give them the jewel, your party receives a ton of AP and some useful items.

If you meet all 8 of them and give them what they want. You get to interact with the Friendly Yan (Sheep looking monster) on Vile Island. When you give this cute little creature what it desires, you get to attack Ozma physically. This benfits Zidane, Steiner, Freya and Amarant.

Some friendly monsters make reference to other friendly monsters, and even give you the right stone to feed to them. This reinforces the fact that there is a certain order in which to encounter the friendly creatures, and the table at the end of this section indicates the order.

Some friendly monster requires special travel system like the chocobo to reach. But once at disc 4 having the Invincible will be a breeze.