The Witching Cloak is a magical item, originally owned by Mister Dark. It later came into the possession of Fabletown. Known abilities of the cloak include unlimited storage space, teleportation across distances and dimensions, invisibility, shape-shifting, and nigh-invulnerability for whoever wears it. It can also be taught to respond to commands. Boy Blue used it in the Homelands. A thread from the Witching Cloak was stuck inside of and plugged up a war injury to Boy Blue, which caused his death when Mister Dark destroyed the entirety of the Cloak, unplugging the wound.
The Witching Cloak is supposed to be all unnamed magical cloaks. Willingham's reason for the different cloaks having different abilities is that the owners might not necessarily explore all the cloak's abilities, just use the one ability they first discover, assuming that it is all the cloak can do (while Blue had lots of time to discover many of the cloak's abilities).