They’re considered down when their knee touches the ground while in possession of the ball (“possession” having a specific meaning, with regard to the rules). Again, this is the same as if they had been tackled. The only difference is no one forced them to the ground.

Taking a knee is not something that would normally be considered a good thing since you lose yards and a down.

As for why it’s not a delay of game, that’s likely because it does not delay the game any more than any normal play would. It probably runs down less time on the clock than if they played normally, but of course playing normally is riskier which why they take a knee. The idea is to simply run down the clock as much as possible without risking a turnover and then leaving the other team with too little time to score.

If the rules could be changed to disincentivize taking a knee I think that would be more interesting, but I’m not sure how you do that. It’s also safer in an already dangerous sport.

Each team has 4 attempts to move the ball forward 10 yards, where if the ball moves >= 10 yards they get a fresh set of 4 attempts. These are called "downs".

If the team has any downs left when they kneel then they can maintain possession of the ball and can thus run out the clock. Most (all?) of the time the teams end the game even if there is time left on the clock.

Note that either team can call a timeout pre-snap which freezes the game clock. Certain plays also result in the game clock freezing between plays. There is also a 2-minute warning at the end of the 2nd/4th quarter that also freezes the game clock.

IMO clock management adds a very interesting strategic layer to NFL football.

Passing the ball around the backfield is a risky tactic in association football (which similarly banned the goalkeeper just picking up backpasses because it was too easy to waste time). 'Taking the ball to the corner' is a much lower risk option, but it is possible to win the ball back and quickly go up the other end and score with good play. Deliberate time wasting between plays is a yellow card offence (even though the referee could simply add the time on, it's disliked)

Plus cricket nominally has more of a sportmanship culture than most sports. "Mankading" (the practice of a bowler deciding to strike the wicket near to him instead of bowling because the runner from the other end has strayed too far[1]) is technically legal and would be considered smart play in many sports - especially since it's an action performed to stop opponents gaining a small advantage over you - but is regarded as shameful in cricket, at least not unless you've been gentlemanly enough to warn the runner at your end to stop straying forward each time the ball is bowled. Indeed it's so controversial Wikipedia maintains a 'list of incidents' page, starting with poor Vinoo Mankad who probably thought he was just being smart and didn't realise his surname would become synonymous with cheating https://en.wikipedia.org/wiki/List_of_Mankading_incidents_in...

[1]baseball fans: roughly the equivalent of a pitcher deciding in mid-pitch to throw the ball to a base to stop someone stealing bases, except the base in question is right next to him.