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The mystical cloak was given to Doctor Strange by the Ancient One after he won his first battle against Dormammu. Doctor Strange has worn the cloak throughout most of his publication history and was a key part of his arsenal.
Doctor Strange had the capability to control the cape through telepathic commands. It could fly on its own and contort itself to the will of Doctor Strange. Doctor Strange often used this to help him defeat some minions of Mordo as in strange tales #143.
Doctor Strange has been portrayed as wearing slightly different versions of the cloak over the years. Such as an almost identical blue cape with no powers, and different other capes in every alternate universe.
Doctor Strange no longer wears the cloak of levitation as he gave it as a gift to one of his students, Rintrah.