Animal lore is very necessary for a tamer. It is impossible for a young tamer to progress far into the profession without it, since they will eventually come to a point where they can no longer control the creatures that they tame.
When you use animal lore, it will bring up a special gump that tells you all about the pet (Page 1, Page 2, Page 3, Page 4, Page 5). This scroll does not update, so when you use animal lore, it will show you everything about the creature at the moment you lored it. To watch the progression of a pet you are training, you will need to lore it often to see the skill/stat level changes.
If you have less than 100.0 animal lore, you can see the lore gump on any tamed creature. At 100.0, you can see the lore gump of any tamable creature (tame or untame). At 110.0 animal lore, you can see the lore gump of any creature in the game.
Animal lore can be raised one of three ways: actively loring tamed creatures, passively while using the animal taming skill, or passively while veterinary healing a creature. While actively loring creatures, you must target a different one each time in order to have a chance to gain.