Black has the initiative and is trying to turn it into a decisive attack on White's king, which is the more exposed of the two. First, let's see how the game went:
55...Be3 56.Rf1 Qd2 57.Rf7 Qxe2+ 58.Kg3 Qe1+ 59.Kf3 Qh1+ 60.Kg3 Qg1+ 61.Kf3 Qf2+ 62.Ke4 Re8+ 63.Re7 Qh4+ White resigned (0-1).
The first impression is that the game took a normal course and ended in victory for Black. David Bronstein, for example, writing in his book Mezhdunarodny Turnir Grossmeisterov, does not query any of the last eight or nine moves. However, a closer examination reveals a dramatic exchange of blunders.
Peelback No. 1
Instead of 56.Rf1?, White should play 56.Rf7!, setting up the threat of 57.Rxb7 mate. Now Black is forced to work with checks; there is no time for a quiet move. Thus: 56...Qg1+ 57.Kf3 Qf1+ 58.Kg3 Bf4+ 59.Kg4. Bronstein reaches this position in his analysis and gives 59...h5+! “et cetera,” with the clear implication that Black is winning.
I always get suspicious when I see a note ending in “et cetera.” I like to carry on the analysis until the win is obvious. In this case there is a problem. After 59...h5+ 60.Kh4 Qf2+ 61.Kxh5 Qxe2+ 62.Kh4 Qe1+ 63.Kh5! there is no forced mate, no forced win of material, and no time for a quiet move. Black can even go wrong: 63...Qe5+?? 64.Qxe5 Bxe5 65.Nd7+ and wins. The first conclusion: 56.Rf7 draws. The second conclusion: 56.Rf1? is a weak move. The third conclusion: 55...Be3 is probably a weak move too.
Peelback No. 2
There is no good reason for Black to allow the move Rf3-f7 until he is ready with a winning continuation. Black can play a move that takes the square g4 away from the White king, so that if White does nothing significant, the attack beginning with Bf4-e3 will be far more dangerous. The move is:
Now White has:
A. 56.Qf7 Bc7! (changing direction in order to give Black's queen access to g5 in some lines) 57.Nd7+ Ka7 58.Nf8 Qg5+ 59.Kf2 Bh2 (also possible is 59...d3 60.Qxc7 Qh4+ 61.Qg3 Qd4+ 62.Kg2 d2 63.Rf1 d1Q 64.Rxd1 Qxd1 and Black is winning) 60.Qg6 Bg1+ 61.Kf1 Qc1+ 62.Kg2 Rd5 63.Ne6 Re5 64.Nf4 Be3 65.Rf1 Qd2 66.Qf7 Bxf4 67.Qxf4 Rxe2+ 68.Kg1 Qxb4 with a winning ending for Black;
B. 56.Qg6 Qd2 57.Rf2 Bc7 58.Qg7 Qe3 59.Qg6 Ka7 60.h4 Qe7 61.Nc4 (unavailing is 61.Qxh5 Rg8+ 62.Kf1 Qe4 and wins) 61...Qxh4 62.Nd6 Qe7 63.Qf6 Bxd6 64.cxd6 Qxd6 65.Qxd6 Rxd6 66.Rf5 Rd5 67.Rf4 d3 68.exd3 Rxd3 69.Rc4 Rd5 70.Kh3 b6 71.Rxc6 bxa5 72.bxa5 Rxa5 and White will have to give up his rook for Black's a-pawn.
I believe the moves 55...Qd2 and 55...Re8 also lead to a win for Black, but the pawn move is less complicated. The conclusion is that Black's move 55...Be3? threw away the win, but White's move 56.Rf1? gave it back.