A double threat means that a player has two different options for achieving a specific goal, usually connecting two groups of pieces. A double threat is a special case (and the most common example) of a multiple threat.
A double threat is also sometimes called miai, a Japanese term taken from Go.
The following is another example. Red's two groups are connected by double threat at the two cells marked "*".
If Blue moves at one of the cells marked "*" or its neighbors, Red can respond at the other one, thus guaranteeing a connection between the two groups.
A ladder escape fork can also be regarded as a kind of double threat.