As black has the upper hand, should white try to go piece-a-piece (Rooks for Rooks) or try and get the two rook endgame.
1r3rk1/p1p2p1p/3p2p1/Rp2p3/3bP1P1/1P1P4/2P3P1/5R1K w - - 0 1
Black has an extra bishop and two extra pawns. Black is completely and easily winning, and white can't do anything really constructive.
Black's easiest way to win is to promote a pawn to queen and then checkmate white; that in turn is easiest if white's rooks are exchanged off (take all rooks off the board, and black just plays a5, a4, a3, a2, a1=Q).
So that's what white should avoid -- if there is a choice, don't exchange the rooks!
That said, resigning is also a perfectly normal action for white in the given position.
Black has an extra piece and 2 pawns, with an extra pawn being on each side of the board. Black has no glaring pawn weaknesses. If the rooks are off the board, White's only chance, and it is a slim one, will be to lock the pawns up in such a way that Black can make no progress. I don't see how he can do it, especially with those doubled pawns on the g file. For example, Black could play
f6 followed by
h5 or work towards
g5 (to lock the white pawn),
f5. White cannot contain the pawns. And that is without taking the Bishop into consideration.
In short, Black wants to get those rooks off the board.