As you complete battles throughout the game, you'll be able to briefly explore your surroundings. Every time this happens, you'll see some animals local to the region. Flexing your Divine Dragon status, you can brazenly steal/adopt these animals at any time and bring them back to the Somniel. Once back at the Somniel, you can select up to 5 of them to graze outside.

Other than just being cute, animals do provide an additional benefit at the Somniel. Every Somniel reset (after battles), every animal that has been grazing outside will magically create a sparkling spot on the ground with an item in it. Different animals can produce different items. For animals that have multiple different possible items, the chance seems to be equal for all items. For example, all dogs have an equal chance of producing an iron, steel, or silver ingot.

The majority of animals in the game can be adopted without any extra work. But certain more rare animals require donation level 2 for their specific country in order to "know how to care for them". All of these criteria listed below.