Why is White's "25. Bh4" considered a great move in Karjakin vs Kramnik at FIDE Candidates Tournament 2018?

Question

I was watching Karjakin vs Kramnik at the FIDE Candidates Tournament 2018, Round 9, and simultaneously observing the chat feed at chess24.com, where people unanimously glorified the move 25. Bh4. Why was it considered such a good move?

[FEN ""]
[Event "FIDE Candidates Tournament 2018"]
[Date "2018.03.20"]
[Result "1-0"]
[White "Sergey Karjakin"]
[Black "Vladimir Kramnik"]
[StartPly "49"]

1. c4 e6 2. Nc3 d5 3. d4 Nf6 4. cxd5 Nxd5 5. e4 Nxc3 6. bxc3
c5 7. Rb1 Be7 8. Nf3 O-O 9. h4 cxd4 10. cxd4 Nc6 11. h5 f5
12. exf5 Qa5+ 13. Bd2 Qxf5 14. Bc3 h6 15. Bd3 Qg4 16. Kf1 e5
17. d5 e4 18. dxc6 exf3 19. gxf3 Rxf3 20. Be2 Rxf2+ 21. Kxf2
Bc5+ 22. Kf1 Qf4+ 23. Bf3 bxc6 24. Be1 Be6 25. Bh4 Rf8 26. Kg2
Kh8 27. Rc1 Rf5 28. Rc3 Rd5 29. Bxd5 Bxd5+ 30. Rf3 Qg4+
31. Bg3 Bd6 32. Rh3 Be7 33. Qe2 Be4 34. Qf2 a5 35. a4 c5
36. Rh1 Bf6 37. Re1 Bc6 38. Ree3 c4 39. Qe2 Qxh5 40. Qxc4 Bd7
41. Rd3 1-0

Answer 1

The reason behind 25. Bh4 is very concrete, namely: With Rf8 coming next for black, white's bound to play Kg2 to unpin and cover f3 but without preparing it with Bh4 it leads to the following forcing variation:

 [title "25. Kg2 without Bh4"]
 [fen "r5k1/p5p1/2p1b2p/2b4P/5q2/5B2/P7/1R1QBK1R w - - 0 1"]

 1. Kg2 Qg5+ 2. Bg3 Rd8 3. Qxd8+ Qxd8 4. Rb8 Bc8 5. Bg4 Qd5+ 6. Kh2 Bd6 7.Rxc8+ Kh7 

This line forces white to give up the queen for the two pieces, and it is definitely still among the winning variations for white but for practical reasons I reckon Karjakin intended to keep his queen on the board and avoid that variation for good, which he perfectly achieves with 25. Bh4 as it stops both Qg5+ and Rd8 and sets up Kg2.

Answer 2

White wants to move his King to g2, but if he does so right away then Black can play ...Qg5+. By playing Bh4, White covers the g5-square, allowing his King to seek haven on g2.

Also, playing Bh4 activates the Bishop (it was extremely passive on e1), and allows White to connect his 3 major pieces after playing Kg2. Overall, just a great multi-purpose move in a position that seems chaotic to handle.