The cloaks are made of a special material that does not reflect any light, which makes them pure black. The invisibility effect was created using brainwashing, by simply telling the people that they could not see pure black. The Shades can see the cloaks due to needing them for their tasks. It is also possible for other people to see the cloak if it is dirty, as this makes them less than pure black.
All the giant machines inside Labyrinthia were hidden using similar cloaking methods. The Bell Tower was initially also hidden under a cloak, but it burned down after being hit by a lightning bolt.