Unremovable Ko Threat
An unremovable ko threat is a ko threat which can't be removed without incurring a loss. Such positions can be one sided or two sided.
When Black needs a ko threat, he takes two stones at A. If White doesn't answer by throwing in again, Black can next atari at B to capture 5 more stones. White can't remove this threat at A because of the suicide rule.
White is allowed to play B, but then Black would capture 6 stones anyway, which is bigger than the threat to begin with.
This is a more complicated example.
Black can play any of the circled points as a threat to turn this seki into 8 points territory. White can't forestall this by playing on either point. Worse: if she does, Black plays one of the other points to make 10 points.
Unremovable ko threats typically occur in seki positions like this one, which is more realistic than the previous. White has a ko threat here at a, which however loses 3 stones and gains Black an extra point, so White loses 7 points by playing the threat.
If Black plays at a himself, White captures to win 17 points. This means White can use this position as a source of ko threats, as long as the ko is more valuable than the 7 point loss. Black can't remove that threat, since, again, White would then capture for free what she would otherwise threaten in a ko.
If the stones involved in the seki are approximately equal on both sides, then the shared liberty at the marked point is equally (un)playable for both. As long as the value of the ko is higher than (here) 17 points, both could play the threat. When the value of the ko drops below 15 points, neither should. The small margin in this example where Black can cause damage which White can't, is practically non-existent.
One can argue that the double ko seki provides such threats but this depends on the rule set. And since the concept of an unremovable ko threat is valid in rule sets that don't rule the bent four in the corner as dead, such rule sets will usually also impose a super ko rule prohibiting using double ko seki as an unlimited source of unremovable ko threats.
Sometimes dead groups contain unremovable ko threats for unremovable kos.