The short answer is: white's making it difficult for black to challenge the center with their central pawns. But that's not really revealing much, so let us dig deeper into this beautiful middlegame.
The rook doubling is in fact part of a grander scheme that Kramnik has in mind. Once black commits to d6, Kramnik targets a very concrete objective:
- To undermine black's control over the
d5 square in order to establish a centralised knight on d5. Ultimately, the plan stems from the asymmetry between the light square control provided by white's center compared to black's central pawn setup (d6-e7). The plan is quite simple in appearance but becomes rather involved once we try to see how it ought to be executed.
Let's now visually unravel the whole thought process behind this plan, but given the question appears to be asked at a basic level, I'll skip certain concrete (tactical) details and only cover the gist of the involved strategic ideas.
So the question is now re-iterated to: How can we establish a knight on d5 without allowing black to easily prevent or trade on d5? and if a trade is to happen on d5, we definitely don't want to have to re-capture with a pawn, which would block a useful central square and potentially gift black a target on d5. Alternatively, you can reformulate the question: How can we turn the d5 square into a safe knight outpost?
Black's control over d5:
Kramnik's surgical strategy:
Left: Reroute knights to d5| Mid: pin the f6 knight | Right: Pressure d6
Left: We need both knights in range of d5 as otherwise in principle black could trade the light square bishop for the knight landing on d5 and white would have to recapture with the pawn, which is exactly what we want to avoid as explained earlier.
- Mid: One of the best defenders of
d5 is the well placed knight on f6, and one way to undermine its defense is to pin the knight by creating a battery along the long diagonal against the fianchetto'ed bishop.
- Right: If black is able to play
e6 without any drawbacks, then they'll have permanently secured control over d5, therefore, by pressurizing the d6 pawn white is making it more difficult for black to play e6 as it would weaken an already targeted d6 pawn.
Notice that in contrast to d5, the b5 square is not as good a post for a knight since not only it is not a central square (knights are strongest when centralised), it is also a square that is quite easy to cover for black as a6 is playable in most cases (unlike e6) thanks to the closed b-file which makes it difficult for b6 to be put under pressure (and thus stop a6).
In summary, with black's 11...d6 commitment, white sets out to establish a well centralised knight on d5, which was harmoniously achieved on move 22.Ncd5:
---->
It must be noted that the knight post on d5 is not permanent, but for as long as the knight can stand centralised without black being able to reciprocate a similar level of minor-piece-activity, white stands favourable - with constant pressure on key squares in black's structure (c7, e7, f6...). That's why Grischuk has tried to counter white's threats by mounting a direct attack on white's king with the rook lift.
Although there's a slight positional edge for white in that final position after Ncd5, it's by no means winning for white, in fact it's just about to get ignited [*], but it is a prime example of Kramnik's positional approach to the game, he always plays with a clear plan in mind, enabled not only by his great strategic intuition for exploiting/spotting weaknesses and calculation capabilities, but also by his tirelessness and resourcefulness in finding ways to improve his pieces. His games cannot be recommended enough to be studied, his purposeful play-style is a unique portrayal of harmony in chess.
[*]: there are many tactical lines that can ensue from the reached position, e.g., Nxd5 Bxd5 Bxb2 Qxb2 Bxd5 Nxd5 and neither Nb6 nor Nf6 are immediately playable (try to figure out for yourself as an exercise). Or Nxd5 Bxd5 Bxb2 Qxb2 Nf6 Bxa8 Qxa8 Rxd6 exd6 Qxf6 (with interesting positional compensation). Or Ne5 Be2 Ne4 ... which is what happened in the game.
