Knockdown has to do with when a character falls over due to taking an attack. This state is known as being “down”, among other names. The act of getting up from this state is termed “wakeup” in fighting game jargon, though the uninitiated (or developers, foreign speakers, etc.) may use terms like “standing” or “rising”.
Largely, one goes tumbling into this state due to sweeps.
In 2D games (the major exception being the combo game subgenre), there generally isn’t a damage hitbox until one gets back up (unless the game allows some sort of on-the-ground attack somehow).
In most 3D and combo games, upright and overhead moves won’t be able to touch, but most low moves and overheads that drop down can (making on-the-ground attacks common).
Relief or not, this state is a bit risky, as if anyone is left standing, they will often be able to transition to meaty attacks. The person who has to get up has the riskier side of this equation: wakeup attacks.
In 3D games, you will often be able to retaliate from this state with wakeup kicks.
As with Lei from the Tekken series, some characters can transition to the downed state as a stance; these characters often perform flavorful techniques (such as groundfighting) this way.