A fork in chess can occur when a long-range piece attacks two or more enemy pieces at the same time (knights and pawns can do so too). It is a maneuver that can be very powerful as shown in the diagram below. After the bishop on a2 captures the pawn on e6, both the king and queen are forked.
For lack of a better term, the "invisible fork" occurs in, for example, the (constructed) position shown in the next diagram. Here, White plays Be6 and forks both the mating square f5 and the rook on h3. It is basically a fork along the same diagonal and is possible because there is no piece on f5 or the "other threat" is invisible. Technically, a fork must involve two forked pieces (typically along two different diagonals) but I would argue that a mating threat (instead of a piece) can be just as bad for the opponent. Furthermore, it would seem that two threats along the same diagonal (one threat "through" another) can indeed exist if one is "invisible" or is not, in itself, an actual piece.
This curiosity was discovered by the computer program, Chesthetica, back in 2008/9 during the development of a computational chess aesthetics model. If you have any thoughts on the subject or know of any other positions like this, please share in the comments below.