The Cloak of Levitation is a magical relic kept by the Masters of the Mystic Arts, specifically in the New York Sanctum, alongside many other relics. It is a red cape with a high collar that allows its wearer to levitate and fly, and has a personality of its own. It is described to be fickle and rare to choose a master, until it found a new master in Stephen Strange. The Cloak becomes Dr. Strange's signature weapon, a powerful artifact that let his control his magic and amplifies it.
The Cloak can also act of its' own accord and is often seen protecting Dr. Strange, whether he is wearing it or not. It can be very persistent, as shown in the film, Dr. Strange when guiding Strange to the Crimson Bands of Cyttorak.