Why is 12. b4 played by a GM? Why doesn't he just capture the bishop? And how can he forsee so far in the future? Am I missing something?
This position is close enough to the beginning of the game that the grandmaster may have already analyzed it at home.
Even at the board it is reasonable to analyze the forcing sequence 12 b4 Bxb4 13 axb4 Qxb4 14 Rfb1 Qe7 (Qd6? 15 Bg3) 15 Qc6 Rb8 16 Rxa7. Now we can pause to evaluate. White has recovered one of the sacrificed pawns and has a very active position, while Black hardly has a reasonable move: both Knights are pinned to the Queen, and any move by Rb8 or Bc8 drops material. White threatens 17 Bg3, attacking the trapped rook, which Black can't free with b5 because after 17 Bg3 Rb6? White can play 18 Qxb6 anyway. If 16 . . . Ne5 White at least has 17 dxe5 Qxa7 18 exf6 winning two pieces for the Rook.
(I'm analyzing this from the diagram, and may well have missed something. But I'm no grandmaster, and never got as high as 2300 USCF before I played tournament chess 25+ years ago. So for an actual grandmaster this kind of analysis should be routine once the GM had made the leap of imagination to consider 12 b4!)
Maybe before justifying the pawn sacs one should answer more convincingly why taking on c3 would not have pleased White. The answer is the backward pawn on c-file and future pressure against it by rooks from c-file. Black cannot be happier if the Queens get exchanged on c3 as well. So, taking the bishop back on c3 would have yielded nothing for White. b4 is half out of desperation as it is of creativity!
Augment to this the forcing sequence delineated by the other answers here, and you see that b4 is not as much of an abnormal move as it may look initially.
If you take the bishop by pawn or queen -- you'll get an equal position with approximately even chances.
b4, and exchanging pawns for a bishop, there's a good attack on queen side, with
Rfb1, then black queen has to find the safe place, and
Qc6 with quite good chances to win a piece.
It's actually a very nice idea. The point is that after:
12.b4 Bxb4 13.axb4 Qxb4 14.Qc6!, White is getting plenty of queenside activity, and is going to win the a7-pawn since Black's rook will have to move to b8. White will still be down a pawn, but will have tremendous queenside activity.
So the point of 12.b4 is that it allows White's queen access to the c6-square, while still winning Black's bishop.
Note that after 12.b4, Black must play 12...Bxb4, or else he just loses his queen since it's trapped.
As for how the GM could have foreseen this, it takes a combination of natural talent and countless hours of practicing calculation to ingrain patterns into the mind. Although I wouldn't say this combination is close to GM calibre, maybe 2200 level at best.
I assume the last move was b2-b4. The idea is 1...Bxb4 2.Rfb1 threatening to trap the queen with axb4. So Bishop somewhere (2...Be7). Now can we trap that queen or something? 3.Rb5 queen a6 is only open square which allows Rook discovery...but I don't see a win here. hmmm, 4.Rc5 Qb7 (4...b5!?) 5.Rc7 Qb8 6.Bg3!?
Okay this line is total junk as pointed out in comments and the answer is far simpler. Black has problems with the unprotected Rook on a8 and it can't find a home on b8 because Bg3.