Originally owned by Ignotus Peverell, the Cloak of Invisibility has been passed down through the generations ending up with the Potter family. It is one of the legendary Deathly Hallows. Many believe it to be the cloak of Death itself, as stated in “The Tale of the Three Brothers”. Dumbledore believes otherwise:
“Whether they met Death on a lonely road…I think it more likely that the Peverell brothers were simply gifted, dangerous wizards who succeeded in creating those powerful objects. The story of them being Death’s own Hallows seems to me the sort of legend that might have sprung up around such creations.” (DH35).
Xenophilius Lovegood tells Harry, Ron, and Hermione what makes this a hallow different from normal invisibility cloaks.
“I mean to say, it is not a travelling cloak imbued with a Disillusionment Charm, or carrying a Bedazzling Hex, or else woven from Demiguise hair, which will hide one initially but fade with the years until it turns opaque. We are talking about a cloak that really and truly renders the wearer completely invisible, and endures eternally, giving constant and impenetrable concealment, no matter what spells are cast at it.” (DH21).
The weave is so fine that an Invisibility Cloak is "strange to the touch, like water woven into material" (PS12).
On Christmas in 1991, Harry received the Cloak of Invisibility anonymously (although later revealed to have been sent by Albus Dumbledore).