Animal Lore affects your ability to control a tamed creature or beast, and also improves the amount of damage you can heal via the Veterinary skill (similar to how Anatomy affects Healing for character healing).
Animal Lore is needed to tame a beast, and it has to be at the same level as the taming requirement, or better. For example, dragons have a taming requirement of 100, which means, you need 100 Animal Lore and 100 Animal Taming. Also, a high Animal Lore skill will reduce the minimum skill required to tame. GM animal lore give you 5 points extra on taming until 80 taming. Above 80, the 5 points starts to lower. A player with 98.1 taming and 100 animal lore should be able to tame everything.
Using the skill directly on a tamed creature will present a listing of its statistics and skills.
To use the skill, open your skill book (press K) and browse to the Animal Lore skill. Press the button to activate the skill, or drag the button to a hotbar to be assigned to a slot.