Animals are randomly generated species on habitable and inner worlds. They are not limited by the same constraints as player made species and can be any size.
Animals also have different habitats such as aerial, aquatic, amphibious, and subterranean. (more info needed here)
When a herbivore walks onto a farm's tile, the farm domesticates that animal. You can then ride that animal around and even bring it with you on your space travels. Planets without animals but with animal farms require the animals to be manually brought to the farms in order for them to work correctly. you cannot domesticate non-herbivores. (More information and details are needed here)