Pelts are a rare and difficult resource to collect in Ark. They are harvested from a select few creatures, most of which inhabit the Snow Biome. At this time, Pelts are used for the creation of the Fur Armor set, which is required to survive in the colder (Snow Biome) regions of Ark.
Pelts are harvested from the creatures inhabiting the Snow Biome. This may well change with future updates, but at the moment if you want fur armor you'll have to brave the cold without this protection.
Mammoths, and Direwolves are a good example of what you need to be hunting to get pelts. Keep in mind that for harvesting pelts the same rules apply as for Hides. A hatchet is the best tool, with Metal being far superior to Stone.
One thing that can really help you endure the cold while harvesting pelts for your Fur Armor is the Fira Curry, which is one of the Rockwell Recipes. This helps increase your resistance to cold.