In short, the key idea is to prevent white from playing h2-h3!

Bc4 forces the exchange of light square bishops, and thus, sets up Rh3 which blocks the h2 pawn and keeps both the h2 and g4 pawns weak. Concretely, the only piece currently covering h3 is the light squared bishop on f1, so by trading the bishop with Bc4, which white cannot prevent as Bg2 leaves h2 hanging, white has no immediate means (e.g. a rook on g3 would prepare h3 but it's too slow) of preventing black's imminent Rh3.

Black's bigger idea is to create two connected central passed pawns!

More precisely, the plan is:

• to pressure g4, and binding white's rooks to the defense of g4 and h2,
• bring the king to e6 to prepare the d5 advance to trade the e4 pawn, then go back to e6 and similarly prepare trading white's g4 pawn with f5,
• after which black is left with a passed f and e pawn, that is, two connected passed pawns!

Suppose Bc4 is not played, then white gets to play h3, and thus maintaining their bind on light squares and killing black's prospect of creating two connected passers. In the game itself, Ivanchuck decided to trade the g-pawn quickly (by advancing it to g5) in order to get rid of one of his weak pawns, after which Anand still managed to execute his plan as all he had to ensure was trading the e4 pawn by playing d5. Here's the position that transpired in the actual game, where Anand's plan has been executed to perfection:

Quite an exemplary game showing Anand's deep positional understanding: note the move Bc4 a priori undermines a couple of chess principles: it willingly trades black's only good bishop, after which black is left with a hemmed-in dark squared bishop vs white's active one. Moreover, black allows their queenside pawns to become shattered into 2 (isolated) islands, and in doing so having less chance of dominating¹ 2-vs-3 on the queenside.

In spite of all these at-first-glance-unfavourable aspects of the move, Anand beautifully realised controlling the h3 square outweighs them all, since preventing white's h2-h3 pawn advance to support g4 is the only way black can maintain the prospect of active play in the pawn skeleton that had transpired, as we discussed above.

^{1: Domination in this context means: the side with the minority (less pawns) achieving a setup (e.g. a blockade) where neither of the majority pawns of the opponent can (easily) advance. Typical to the Sicilian pawn structure on the queenside, one such setup could be white's pawns being on a2-b3-c2 and black's pawns pinning down on dark squares with a5-b4. For an example see the setup by Caruana (as black) in his candidates game vs Karjakin (e.g. around move 22), where indeed one of his positional mistakes in that game was to give up the domination with 26...a4.}