An Invisibility Cloak is a cloak of silvery grey material that, when worn, makes the covered parts of the wearer invisible. Invisibility Cloaks are rare and valuable.
Invisibility Cloaks can be created in at least three different ways. Some are imbued with a Disillusionment Charm, some carry a Bedazzling Hex, and some are woven from Demiguise hair. Such cloaks fade over the years until they turn opaque (FB, DH21).
Harry inherited one from James Potter, which was given to him anonymously by Albus Dumbledore at Christmas of 1991 (PS12). Harry's Invisibility Cloak is actually a unique artefact, one of the Deathly Hallows (DH). Part of its magic is that it expands to protect not only the wearer but others as well. It can cover several kids and a dragon in a wooden packing crate, for example (PS14).
The fake Moody had an Invisibility Cloak in the seven-lock trunk (second key) (GF35). The members of the Order of the Phoenix used invisibility cloaks to hide themselves as they stood guard over the Department of Mysteries (OP26)