Animals (a.k.a. Beasts) are one of the three major enemy types in Diablo series, among with Demons and Undead.
Animal class refers to any wildlife, usually native to Sanctuary (i.e. not demonic or angelic). Some animals are even intelligent or semi-intelligent, and may even use magic. A corrupted wildlife form may or may not be an Animal, however, a savage demonic creature will not fall into this category.
Many animals are larger and stronger than Humans, and some of them (like Beasts) were even tamed by mankind. Others are hunted or just avoided contact with.
Khazra, which are corrupted humans in essence, count as Demons in the second game, but as Beasts in the third game.
Undead may be risen from Animal remains if needed.
Diablo I
In Diablo I, Beasts are resistant to blunt weapons, but weak against sharp blades. Scavengers, Spitting Terrors, Bats, Horned Demons and most creatures in the Hive are Animals.
Diablo II
In Diablo II, Beasts do not exist as a marked category, but many enemies will count as Animals: Blood Hawks, Sand Maggots, Wendigo, Giant Spiders and Swarms, to name a few. They no longer receive altered damage from any specific weapon types.
Diablo III
In Diablo III, Beast enemies are a separate category, and include Khazra in addition to many animals. Pig Sticker and Monster Hunter are specifically designed against Beasts.
Ancient Beasts is a separate type of monsters, completely independent from Animals, and refers to the wildlife of Pandemonium.