Here's how it seems to work, at least as far as my experiments have been able to determine:
The world map is broken up into biomes, of which there are several dozen different types. Each individual biome also has a level of savagery (benign, neutral, savage) and alignment (good, neutral, evil). Each biome may stretch over many embark tiles. When you embark, you can see a list of all the biomes your embark site intersects on the embark screen.
Each creature has a list of biomes it can be found in, as well as a starting population number. Creatures can also have [GOOD] and [EVIL] tokens, and those will restrict those creatures to appear in good or evil biomes. Creatures with the [SAVAGE] token can only appear in biomes with high savagery. The [BENIGN] token is a bit different, in that biomes with low savagery will only have [BENIGN] creatures, although [BENIGN] creatures can appear in biomes of any savagery level.
When the world is created a population of wandering wild animals is created for each biome according to this number. During gameplay these creatures will randomly wander on and off your map. When they enter they are taken from the biome population, and when they leave the map they are added back to it. This population may breed over time, increasing the number, although that may be limited to animals with the [PET] token, such as horses and elephants. As far as I can tell if you completely wipe out the local population of a type of animal, it never recovers.
So, if you want to maximize the number of wild animals you'll see, you want to look for biomes which the most creatures can appear in. Forests in general are good, especially "Tropical moist broadleaf forest" which have a huge number of creatures which can appear in them. Avoid Benign biomes (Serene/Calm/Sinister), they have far fewer creatures which can appear. High savagery, and either good (Joyous Wilds) or evil (Terrifying) if you want to also get the creatures which specifically appear in only those biomes. Choosing a fortress site which spans several biomes also seems to help, as you get the populations of each to draw from.
Of course, since the population of local creatures is finite, and it appears that at the moment only creatures with the [PET] tag breed, you're going to run out of wild animals to hunt eventually no matter what.