The Invisibility Cloak is a cloak which turns the wearer completely invisible. Harry gets it as a Christmas present from Albus Dumbledore, who had it in his possession since shortly before it's previous owner died. This previous owner was Harry's father, James Potter. Harry frequently used his cloak to explore Hogwarts at night.
The Invisibility Cloak is a shiny, silvery robe – smoother than silk and extremely light. The cloak turns its wearer invisible.
Harry owns an Invisibility Cloak; it is a family heirloom which he is given for Christmas during his first year. He uses it mostly to explore the castle after hours.