Professor Elwyn Berlekamp coined the term, komaster, for the person who can win a ko (or superko) fight without having to ignore a ko threat. The opponent is the koloser. It is possible, of course, that a ko has neither komaster nor koloser.
(The above is an informal explanation. For Berlekamp's original treatment, see http://www.msri.org/publications/books/Book29/files/ber.pdf.)
For certain kos, such as approach kos and ten thousand year kos, the count depends on who is komaster. Such kos, and similar ko positions, are called "hyperactive". In some ko positions, who is komaster does not affect the count, but does affect the miai value; Bill Spight coined the term "active" for such positions. Other ko positions are called "placid".
Note that the komaster won the ko after using only one ko threat. That threat was enough to make her komaster. If a komaster can gain from using additional ko threats to delay winning the ko, she is ko monster.
When Bill talks about "ko threats" here, I believe he is basically referring to sufficiently big sente moves. If a gote move is big enough to distract your opponent from finishing a ko, then it suggests that the ko was probably too small to be worth fighting yet. If big gote moves are the best "ko threats" you can find, then by this usage, you have no ko threats.
Some ko fights, including many ordinary direct kos, don't require ko threats, because the alternative to winning the ko is just as good -- this is often true, since kos become interesting when they have roughly the same miai value as the biggest plays elsewhere. If losing the ko is as good as winning it, then why waste ko threats you might need later?
Ko threats become important when ordinary moves elsewhere are worth less than winning the ko. When you're fighting that last tiny ko that ends the game, the ambient temperature is zero. When a complex situation turns into an all-or-nothing ko, that ko may be very hot. And as Bill discussed, turning an approach ko into a direct ko can raise the local temperature.
Hyperpape: So the definition of ko threats adopted here are plays above the ambient temperature?
Bill: I am not sure what you are asking. The definition of komaster does not specifically mention ko threats. To translate into something more concrete, we can say that the threats are big enough for the komaster to win the ko with correct play. It happens that just being hotter than the ambient temperature is not necessarily big enough. I know that that is vague, but one of the charms of the komaster concept is that it allows us to draw specific conclusions from vague premises. ;)
Hyperpape: Not the definition, but the informal explanation at the top of the page? As for the idea that ambient temperature was the key concept, I thought I got that from EricB's paraphrase. In any case, I'm trying to conceptualize the komaster, and see if there's a relation to the primary/secondary ko threat distinction you draw elsewhere.
Bill: All of the komaster's threats must be primary threats, and he must have enough to win the ko (and perhaps other kos) but not enough to cause the temperature to drop. Maintaining the temperature may require defensive ko threats by the koloser.
Hyperpape: In the case where the komaster can wait for the temperature to drop, he's komonster, then?
Also see virtual-force.