Reversible Moves are all moves by pieces (except pawns) to empty target squares, thus the complement set of the irreversible moves of captures and pawn moves (including promotions). Making reversible moves increments the halfmove clock inside a chess position object, concerning the fifty-move rule.
Reversible Moves in this sense may otherwise not strictly reversible if they lose the castling rights, that is rook- and king-moves from their initial squares, including castling itself. They are irreversible in the sense of reversing the same rights - since once a castling right is lost, it is lost forever, as considered in detecting repetitions. However, those moves don't reset, but increment the halfmove clock as well.