Mutual ko threat
A mutual ko threat is a local position in which either player, moving first, has a ko threat, such that playing the threat removes the other player's threat. Usually a mutual threat is a miai in which each player makes a play, regardless of who plays first.
In this position, a and b are miai, Both players must get one of them in order to live. Either by getting two eyes or by getting seki. If it is White's turn to find a threat, white can play b, to which black must respond a, or a, to which black must respond b. The same goes for black
In this position Black typically gets a and White gets b. Either Ba or Wb may be used as a ko threat, threatening to gain 6 points in two moves.
At times, the double ko threat is one in which the same play by either player carries a threat.
In this example, a is a mutual ko threat. When either player plays at a, it threatens kill the other player's group by cutting it into two.
Typically a player should play the mutual ko threats before starting a ko fight, to prevent the opponent from playing them. So these "double threats" don't normally play any part in ko fights. See remove double threats before you first capture the ko.