First, a little meta-analysis of the consequences of White's break with c5. After 1. c5 dxc5 2. Kxc5, White has two plans: to wheedle his king into e5, or to play d6. In either case the ultimate objective is the black K-side. If Black plays 2 . . . Ke7, for example, the idea would be 3. Kc6 Kd8 4. d6 cxd6 5. Kxd6. If that turns out to win for White, it means that Black must answer Kxc5 with Kd7. White's other idea involves playing the king to d4 then e5. If that is effective, Black must prevent it by meeting Kd4 with Kd6.
Whether these plans win depends on the K-side pawn structures, but if both are effective, Black must meet Kc4 with Ke7 (to stay in contact with e7 and d7). This defence by related squares runs out when we consider c3 and d3. If the white king plays to either of those (threatening Kc4 or Kd4), Black needs his own king to move to d7 (in touch with e7 and d6). And how can he move his king to d7 if it is already on d7?
By playing 1. h3] Speelman found a way to set his opponent problems. Black has three options: a) to stop g4 with h5; b) to prepare g5 himself by playing h6; c) to do nothing. Only precise analysis can determine which is correct. 1 . . . h5 looks fishy, since it uses up Black's spare move, leaving White with a free move in h4 if he needs one. Analysis confirms that it loses: 2. c5 dxc5 3. Kxc5 Kd7 4. Kc4 Ke7 5. Kc3 Kd7 6. Kd3] Ke7 7. Kc4] Kd6 (or 7 . . . Kd7 8. Kc5 Ke7 9. Kc6 Kd8 10. d6) 8. Kd4 Ke7 (or 8 . . . Kd7 9. Kc5] as before) 9. Ke5 Kf7 (9 . . . Kd7 10. Kf6 Kd6 11. Kxg6 Kxd5 12. Kxf5 c5 13. g4 leads to a won queen and pawn endgame) 10. d6 cxd6+ 11. Kxd6 Kf6 12. h4] Kf7 13. Kd7 Kf6 14. Ke8 Kg7 15. Ke7 Kg8 16. Kf6 Kh7 17. Kf7 Kh6 18. Kg8] and White wins.
Black played 1 . . . h6, but after 2. g4] realised that 2 . . . fxg4 3. hxg4 h5 would lose to 4. f5] hxg4 5. fxg6 Ke7 6. Kxc7 g3 7. c5] Equally, in this line, 3 . . . Kc8 would lose to 4. f5 gxf5 5. gxf5 h5 6. f6 Kd8 7. f7 Ke7 8. Kxc7.
The game continued 2 . . . Kc8 3. gxf5 gxf5 and now the standard recipe: 4. c5 dxc5 5. Kxc5 Kd7 6. Kc4 Ke7 7. Kc3] Kd7 8. Kd3] Ke7 9. Kc4] and Black resigned. He is lost after either 9 . . . Kd6 10. Kd4 Ke7 11. Ke5 or 9 . . . Kd7 10. Kc5 Ke7 11. Kc6 Kd8 12. d6. Black could have drawn by keeping his nerve after 1. h3. The right reply is 1 . . . Kc8] and the reason it works is that 2. g4 can be met by 2 . . . g5] when 3. fxg5 f4 is good for Black, while 3. gxf5 gxf4 4. f6 Kd8 5. f7 Ke7 6. Kxc7 f3 is now too slow for White. A difficult endgame, but Black should have been able to work it out.