Cutting the defending king off along a rank is far stronger than along a file. Even a rook pawn wins when the defending king is held on the back rank by a rook on the seventh.
A rook pawn normally offers the defender excellent drawing chances, but here the black king is cut off along the eighth rank. White's rook on a7 is on the right rank, and only has to do it from a square that does not block the pawn: 1.Re7!. The rook keeps the whole seventh rank, so the black king on g8 can never come down the board, and it also frees the a-file for the pawn.