The position comes from the game Lerner - Dorfman, USSR Championship 1980. The late Konstantin Lerner found the only winning move, which is 71.Rf2!!
The reason it wins is best explained by looking at why the obvious alternative fails. After 71. Kb7?, Black draws by employing the well-known technique of "shoulder-charging", to keep the white king at bay: 71...Kf6! 72. Kc6 Ke5! The white king is unable to get back to help stop the pawn. The position is drawn after 73. Kc5 g4 74. Kc4 Ke4 75. Kc3 g3 76. Rh8 g2 77. Rg8 Kf3 78. Kd2 Kf2, etc.
Once one has seen that, the logic of Lerner's move becomes clear. 71.Rf2!! stops the black king from shoulder-charging the enemy king away, and the white monarch is thus able to return in time to help stop the pawn, even though White's first move looks as though it loses a tempo. The game ended 71... Kh6 72. Kb7 g4 73. Kc6 Kg5 74. Kd5 g3 75. Rf8 Kg4 76. Ke4 1-0
The solution is simple enough once one sees it, but it takes a fine endgame player to find such an idea over the board. Lerner was a very fine endgame player, as shown in the article by Yochanan Afek in the September issue of Chess (Britain's leading chess magazine), which presents a number of instructive endings by the late Grandmaster, who spent his last years in Israel.
Both the article and the whole issue of the magazine (John Saunders' last as Editor) are excellent, and I recommend them.