Knockback is a measure of how far an attack sends its target. For example, Bowser's forward smash is an attack of high knockback; it launches opponents very far, so far that at high damages it's more powerful than a Home-run Bat's smash attack. Pikachu's neutral A, on the other hand, has very low knockback - it hardly sends opponents anywhere.
The knockback of most attacks increases as the target's damage increases; however, there are some exceptions, notably Fox's Reflector in Melee. Attacks like this are said to have set knockback (see below). There are also some attacks whose knockback is disproportionate to its damage. For example, Ganondorf's Warlock Punch does more damage than Jigglypuff's Rest attack, yet the Rest has a much higher knockback. Also, attacks knock back light characters farther than heavy characters.
In-game, knockback is measured from 0 (target goes nowhere) to over 60,000 (Critical Hit at 300%). A knockback from 5,500 to 6,500 will often KO characters. The unit is given in match results as "mph"; while this would presumably mean "miles per hour", 1,000mph barely sends characters anywhere, so it's obviously an arbitrary measure.
An attack with set knockback (also called recessive knockback) knocks its target back a specific distance that is unaffected by the target's damage. The most famous attack with set knockback is Fox's Reflector in Melee. Other examples include Luigi's taunt, the first hit of Young Link's forward smash, and Falco's blaster. Some attacks, such as Ness' forward throw and some Natural combos, have set knockback up until a specific point at which the knockback becomes dependent on damage.