The Fur bed is a type of bed made with fur and acts like a normal bed. This bed is very useful for when the player can't find any wool. There are no known places where it can be naturally found. There probably aren't any (yet).
Note, that player respawning is changed by the mod. Follow the link for more details.
The bed can be crafted on a normal crafting table with three fur and three wooden planks of any kind.