In chess, a "royal fork" is a specific type of fork in which a single piece, almost always a knight, makes a move such that it simultaneously attacks both the opponent's king and his queen (the two "royal" chess pieces).
A royal fork is extremely powerful, not only because it simultaneously attacks the two most important pieces, almost certainly ensuring the capture of the queen, but also because by putting the king in check (especially with a knight) the king is required by rule to move out of check, and therefore there is no time to save the queen by launching a counter attack somewhere else on the board.
In a normal fork, even one involving the queen, it is often possible to escape with no damage by launching an even greater threat elsewhere, such as putting the opponent's king in check. However in a royal fork, this is not possible, because one's own king is in check.