A NetHack wand that does what it says: it makes things invisible. Actually, it just makes living things invisible, such as yourself or nearby monsters. I don't believe it can be used on items or dungeon features (such as doors).

This wand is easily mistaken for a wand of teleportation for two reasons. First, if a monster has one and zaps itself, the monster will suddenly disappear as if teleported. If you see this happen, attack again in the direction of the monster's last known location.

Second, when you engrave with a wand to identify it, and the text you're adding on to disappears, the wand could be either a wand of make invisible or a wand of teleportation. In the latter case, the writing that was on the floor is transported to another location on the level; look for it (although this is tedious). If you cannot find it, you have an invisibility wand.