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 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 shine. Attacks like this are said to have set knockback. There are also some attacks whose knockback is disproportionate to its damage. For example, Marth's fully charged neutral-b does a similar amount of damage as Jigglypuff's Rest attack, yet the Rest has a much higher knockback. Also, attacks knock back light characters farther than heavy characters.