Knockback is an element of gameplay and a type of Crowd Control effect, usable by both players and monsters.
The general concept is forcibly moving the target backwards on a successful hit. This makes the target leave the melee range and be briefly unable to perform any action (while moving).
General rule is that Knockback does not work on most Bosses. If a weapon or item has the Knockback modifier, any hits that landed upon a target will knock the target back a certain distance. If the target is against a wall or another obstacle, it will not be knocked back. The distance is set so multiple knockback modifiers have no effect. The target must be hit to knock it back, missing will do nothing.
Knockback can be either helpful or detrimental, depending on the situation your hero is in. If, for example, the hero is a ranged physical attacker, such as the Amazon, or a Throwing Barbarian, Knockback is helpful because most monsters will not be able to reach you, leading to surviving many fights without the need for healing. On the flip side of the coin, if the character is a Zealot, Knockback may be a bit more annoying, as your specialties lie in fast, powerful melee strikes. Knocking said enemies into a wall can remedy this, and in addition, causes their hit recovery animations to begin, effectively 'stunlocking' with no ability to retaliate. With some really bad luck, the same thing can be done to players by enemies.
Diablo
In the original Diablo, players could have obtained the items with Bear suffixes, which causes each successful hit to push the victim back. With a high enough degree of Attack Speed, it allows for keeping the enemy from approaching the hero, making ranged characters nearly invulnerable to attacks of single melee monsters. For melee heroes, however, it could easily backfire, helping the ranged enemies escape the player.
The Telekinesis spell also knocks back enemies but does not work against some Super Uniques.
Some enemies could use this trait as well: for example, the Horned Demons' and some Goatmen's charge, or Diablo's attacks. This could be countered by standing against a wall.
Diablo II
Knockback was greatly expanded in Diablo II. In addition to the Bear affix on items, it was built into some skills, such as Sorceress' Telekinesis. Many monsters also have this ability, or at least special attacks with it, such as Baal's wave spell.
Knockback is also a Special Modifier.
Although Knockback works on most monsters in the game, Act Bosses/Uniques possess full immunity to it.
Diablo III
In Diablo III, Knockback can be found on items (as an X% chance to Knockback on hit) or is in-built into skills as either a guaranteed consequence of a damaging hit or as a chance of such.
Monsters can have a Knockback trait (see the respective article) that gives them a chance on any damaging attack (including other affixes) to send the player flying, throwing them backwards a random distance and slowing them down for a short time.
Some monsters have a guaranteed Knockback for some attacks, such as Death Maidens' whirling blow. For the balance purposes, players cannot be knocked back more than once every 6 seconds. Monsters build up the crowd control resistance as they are continuously knocked back, but instead of reducing effectiveness of subsequent Knockbacks, they simply become immune to it at 65% or higher.
In Diablo III, Knockback can push the target through other enemies (or allies), but not through impassable terrain and not through walls. Unless stated otherwise, Knockback does not add Stun and Slow. However, while flying, a knocked back target cannot perform any active actions (unless those are specifically stated to be usable while stunned, such as Diamond Skin), effectively being paralyzed. Attacking a target in flight is possible, but can be challenging in terms of aiming.
Equipping Krelm's Buff Bracers will render player immune to both Stun and Knockback.
There is even a special type of Knockback called Knock Up. This does not move the target, but leaves it paralyzed (and vulnerable) for a very brief time. Another special type of Knockback is pulling the target to the attacker (sort of reversed-knockback, like the Vortex monster affix). Pulling enemy back also stops if they hit a solid wall, but can pull them through other enemies.
Obviously, for the purpose of effects that require the target to be standing still or moving for a certain time or distance, Knockback does count as movement.
Monsters whose animation does not imply they can normally move (such as Rockworms and Scavenging Tunnelers) are immune to Knockback. However, the mere of fact of the monster being immobile does not make them immune to Knockback: for example, one can kick a Summoner of the Dead from its own summoning circle. Also Knockback has no effect on very large creatures, such as Colossal Golgors or Punishers.