Why did Black resign?

Because the pawn on c6 has the black rook tied up and white is moving his bishop to c7 which will free up his rook. Once white can move the rook, he can force the trade of rooks and then the pawn can't be stopped by black.

I'd suggest not to exchange the rooks but to move the wK to the queen side over the dark squares. And finally invade the black position with the help of his free rook.

I don't like to exchange rooks as black can defend the rook on b7 by Bc8. If white captured on b7, an opposite color bishop ending with one pawn advantage looks insufficient to win.

White moves B-c7, blocking in black's rook.

Remaining pieces are advantage white, as rook better than black bishop, and white has more moveable pawns.

,,