(From 5th Edition Monster Manual - 2014):

This monstrous predator takes its name from its ability to displace light so that it appears to be several feet away from its actual location. A displacer beast resembles a sleek great cat covered in blue-black fur. However, its otherworldly origins are clear in its six legs and the two tentacles sprouting from its shoulders, both ending in pads tipped with spiky protrusions. A displacer beast’s eyes glow with an awful malevolence that persists even in death.

Unseelie Origins. Displacer beasts roamed the twilight lands of the Feywild for ages, until they were captured and trained by the Unseelie Court. The warriors of the court selectively bred the beasts to reinforce their ferocious and predatory nature, using them to hunt unicorns, pegasi, and other wondrous prey. However, it didn’t take long for the displacer beasts to use their malevolent intelligence to escape their masters.

Running and breeding freely in the Feywild, the displacer beasts soon came to the attention of the Seelie Court. With blink dog companions at their side, fey hunters drove these predators to the fringes of the Feywild, where many crossed over to the Material Plane. To this day, displacer beasts and blink dogs attack each other on sight.

Love of the Kill. Displacer beasts kill not just for food but also for sport. They target prey even when not hungry, often toying with their victims to entertain themselves until they are ready to eat. After killing its prey using its tentacles, a displacer beast drags the corpse to a quiet place where it can feed without distraction.

Displacer beasts hunt alone or in small prides that demonstrate skill at setting ambushes. A single beast will strike and withdraw, luring prey into a densely wooded area where its packmates wait. Packs of displacer beasts hunting near trade roads recall the frequency and schedule of regular caravans, laying down ambushes to pick off those caravans.

Prized Guards and Pets. Intelligent evil creatures favor displacer beasts as pets, but a displacer beast enters such an alliance only if it appears beneficial. A displacer beast might guard a vault or act as a bodyguard for a prominent individual.

(From 3.5e Monster Manual - 2003):

This creature looks like an emaciated panther, with blue-black fur, six legs, and a body that is nothing but muscle and bone. A pair of tentacles sprout from its shoulders and end in horny-ridged pads. 

The displacer beast is a savage and stealthy carnivore that resembles a puma in some respects. 

Displacer beasts favor small game but will eat anything they can catch. They regard all other creatures as prey and tend to attack anything they meet. They have a deep-seated hatred of blink dogs, and the two attack each other ruthlessly when their paths cross. A displacer beast is the size of a Bengal tiger, about 9 feet long and weighing about 500 pounds.

 Displacer beasts speak Common.

Combat: Displacer beasts tear at opponents with their tentacles and bite foes that get close. 

Displacement (Su): A light-bending glamer continually surrounds a displacer beast, making it difficult to surmise the creature’s true location. Any melee or ranged attack directed at it has a 50% miss chance unless the attacker can locate the beast by some means other than sight. A true seeing effect allows the user to see the beast’s position, but see invisibility has no effect. 

Resistance to Ranged Attacks (Su): A displacer beast has a +2 resistance bonus on saves against any ranged magical attack that specifically targets it (except for ranged touch attacks). 

Skills: A displacer beast has a +8 racial bonus on Hide checks, thanks to its displacement ability. 

Displacer Beast Pack Lord: Due to the bizarre nature of their anatomy, displacer beasts are unusually likely to produce mutant offspring. These whelps can grow to tremendous size, reaching a length of 20 feet and standing almost 10 feet high at the shoulder. Pack lords, as these gigantic displacer beasts are known, frequently lead bands of their smaller fellows. Except for their freakish size and strength.

(From Monstrous Manual - 1993):

The displacer beast is a magical creature that resembles a puma with two powerful black tentacles growing from its shoulders. Very rare, they stay far from human habitations.

The displacer beast has the blue-black coloring of a dark panther,and a long cat-like body and head. Females range in length from 8 to 9 feet, and weigh 450 pounds; males are 10 to 12 feet long, and weigh up to 500 Lbs. They have 6 legs. Tentacles are tipped with rough horny edges that can inflict terrible wounds. Their eyes glow bright green, even after death.

Combat: The displacer beast is a fierce, savage creature that hates all forms of life. Highly aggressive, the displacer beast will attack on sight, using its tentacles to inflict 2-8 (2d4) points of damage to its victims.

Their main advantage in combat is their magical power of displacement, which allows them to appear to be some 3 feet from their actual location. Anyone attacking a displacer beast does so at -2 on his attack roll. In addition, the beasts save as 12th-level fighters; adding +2 to their die rolls.

To determine the true position of the displacer beast and its illusion, roll 1d10. On 1-5, the illusion is in front of the creature, 6-7 to the creature’s left, 8-9, to the right. On 10, the illusion is behind the beasts actual position. Although this ability is magical, the beast�s location can not be determined by dispel or detect magic. Only true seeing will reveal its position.

Displacer beasts will not use their claws or teeth unless near death, or when in combat with a very large opponent. If they do employ them, each claw does 1-3 points of damage, and each bite does 1-8 points of damage.

Habitat/Society: Displacer beasts are carnivores. Unless they are raising young, they usually run in packs, carving a savage swath of destruction as they go. They hate all life, and will sometimes kill purely for pleasure. Fierce and vicious as they are, however, displacer beasts never fight among themselves. The pack is a well-run and highly efficient killing machine. When encountered in packs, displacer beasts are more than a match for many large creatures and have been known to make a meal of orcs, goblins, and bands of men. Any creature entering their territory is viewed as potential prey.

Displacer beasts mate in the autumn, and the young are born in spring. A mated pair of displacer beasts makes its home in a cave, producing litters of 1-4 young. The cubs, about the size of domestic cats, are born without tentacles and reach maturity, though not full size, within 4 months. They remain in the cave until their displacement abilities are fully developed. This is followed by a two month period during which the cubs are taught how to hunt. When this is completed, the family group disbands and the monsters wander off to join separate packs. While raising young, the monsters are fiercely protective of their lairs. One adult always remains with the cubs, usually the female, while the other goes off to hunt. Dead prey is dragged back to the lair to be eaten by the family. Lairs are littered with the bones, equipment, and the treasures of its victims.

Naturally vicious and almost evil at times, displacer beasts harbor an undying hatred of blink dogs. Many theories attempt to account for this enmity. Some sages believe it springs from antipathy in temperaments — the lawful good blink dog would naturally be the enemy of a creature as savage and destructive as the displacer beast. Others argue that it is the displacement and blink abilities which cause this antipathy — the two abilities, when in close proximity, somehow stimulate the nervous system and produce hostile reactions. Encounters between the two breeds are rare however, since they do not share the same territory.

Ecology: Displacer beasts have little to fear from other large predators, save perhaps trolls or giants. Some wizards and alchemists value their hides for use in certain magical preparations, and will offer generous rewards for them. The eyes of a displacer beast are a highly prized, if uncommon, good luck charms among thieves who believe that they will protect the bearer from detection.