This allows Black to keep the queenside closed whichever pawn, a or b, White advances. This very much resembles the outcome of Petrosian's 1 8 . . . a6 ! in his 7th match game against Spassky in 1966. Now Black still has a long way to go on the kingside, but at least his king, unlike the white one, is out of the way, and he later managed to outwit his opponent.

After a bad opening, there is hope for the middle game. After a bad middle game, there is hope for the endgame. But once you are in the endgame, the moment of truth has arrived."
– Edmar Mednis.

Heading for an endgame can also be a valid reason for taking your king for a stroll. In the diagram position, the queens are very likely to disappear from the board, and because of that, Black would prefer to keep his king in the center, for instance on e7. Apparently, Anand was not satisfied with that and sent his king towards c7, where it also defends the pawn on b7.

23.Rfb1, vacating f1 for the knight, was an alternative.

It's not much of a pawn that White wins, considering his doubled c-pawns. Although he disposes of his bad bishop, it is Black who obtains the active pieces.

Here the advantage of already having the king on c7 is obvious. Thus the king walk has yielded Black a slightly improved version of the endgame that was to come. Later Anand had a real winning chance before the game ended in a draw.

As you may know, the location of the king is crucial in positions with only major pieces. Having the initiative against a vulnerable king is a big advantage in such positions. No wonder here we see the occasional stroll to the opposite side. Here Black has the upper hand, but he still has to break through on the kingside. In order to do so, he first brings his own king to safety. This strongly resembles Petrosian-Unzicker, Hamburg 1 960, where the future World Champion, in a superior position, first brought his king from g1 to b1 before starting an offensive on the kingside.

Perhaps the more active 38.f4 was worth a try, while 38.a6 seems useful to include, to obtain some entry squares ( c6 at least) for the queen.

The queen threatens to enter the queenside, exposing the white king.

Finally, but also decisively!