Animal Fat is collected either by killing and harvesting certain animals with a stone hunting knife or as a passive income from a different Animal Pens. It is a essential material mainly used to quench armor and weapons in a Quenching Pool. Also for other things like Fishing Bait, Fiery Oil, Venom and Fertilizer.
If you want to increase the income of ressources from harvesting, you will have to craft better tools. Check out this guide about tools to be more efficient in Myth Of Empires.
You can obtain Animal Fat harvesting the corpse of certain animals: Boar, Wolf, Bear, Panther, Tiger, Crocodile, Rhino and Elephant. Horses, Rabbits, Foxes and Deers wont give you Animal Fat.
The slower method to get it is to kill and harvest the mentioned animals with a Stone Hunting Knife. The probability of obtaining Animal Fat from harvesting are low, but the chance is there.
The much more effective way to get Animal Fat is by building a Animal Pens. Catch and breed Animals to get a permanent passive income of Animal Fat and other resources if you feed them.
Once you hit level “33” you can unlock the Boar Pen. Its the first Pen that provides you with Animal Fat. Press “P” to open “Crafting & Recipes” and unlock “Animal Pen”.
Check out this guide to learn more about Pens and how to catch and breed Amimals.