Fur Pelts are dropped by various mobs when they are killed by the player or natural death.
Foxes drop fur pelts.
Usage
With fur pelts you can make fur cloth armor or Leather. Simply craft the fur armor as if you were crafting regular armor, but with fur instead of whatever. Also, when crafting fur pelts to make leather, you will also get one fiber, which can be collected to make string. This is similar to making wool but yields only one string.
Leather
Fur Cloth Helmet
Fur Cloth Tunic
Fur Cloth Leggings
Fur Cloth Boots