That is the rook that is on the 1st rank.
Say you have one rook on a1, and the other on a5. If one of them moves to a3, you can't write Ra3, since you wouldn't know which rook it was. So you'd write R1a3 or R5a3 depending.
Similarly with files: if you have a rook on a1 and one on e1, and one of them moves to c1, you write Rac1 or Rec1.
In case both apply, you use the file, not the rank. So in the common case of knights on b1 and f3 and one of them moving to d2, you write Nbd2 or Nfd2, not N1d2 and N3d2.
I'm reading a chess book and sometimes I come across R(1)-wherever. Which rook is (1)? Thanks!!