The displacer beast is a feline monster new to SLASH'EM and included in dNethack. Every time you attempt to attack it in melee, you have a chance (around 1/2) of merely displacing like a pet. Using F to force an attack will not move you (or the displacer beast) and will give the message "You attack thin air" if you would have displaced it.
Displacer beasts can pose a real problem in combat. Not only do they have the displacement property, which renders around half your melee attacks harmless, they also have a very low armor class and many hit points. In addition, they do a fair amount of physical damage. Luckily, they are not fast, and a player with speed should be able to outrun them. This is particularly advisable if there are other monsters around, for displacing them uses a movement, possibly allowing the displacer beast and any other monsters around a free chance to attack.
Amusingly, in SLASH'EM you can displace a displacer beast into water or lava, killing it instantly ("The displacer beast drowns" and "The displacer beast burns to a crisp", respectively). In dNethack displacer beasts have flying, and so are not affected by these squares.
The displacer beast, in D&D, is a monster that projects a displaced image a few feet from where it actually stands. It is the source mythology for the displacement provided by the cloak of displacement.