Zapping a wand of make invisible makes the target monster invisible. If you zap it at yourself, you become permanently invisible, unless you are wearing a mummy wrapping. Zapping the wand downward on a square with an engraving will make the engraving disappear.
In SLASH'EM, wands of make invisible can also make objects invisible. This simplifies the process of identifying the wand.
The invisibility can be circumvented by wearing a mummy wrapping.
Wands comprise 4% of all randomly-generated items in the main dungeon, 6% in containers, 5% on the Rogue level, and 8% in Gehennom. There is a 4.5% chance that a randomly-generated wand will be a wand of make invisible.
See the main article Invisibility for advantages, disadvantages and tactics of becoming invisible, especially interaction with shops. If you do not yet have a method to enter shops, you might want to keep this wand in case you get a fresh stalker corpse in order to get permanent invisibility and see invisible.
After a player is permanently invisible, this wand normally has little use. In particular, making your non-steed pets invisible does not give them a combat advantage.