The point is that Black cannot castle. White's pawn on c3 could not have captured either of Black's missing pawn, which never could have reached the c-file. (Black has made only two captures, one of which was on f6). The Pc3 cannot have captured Black's QB either, which could never move to c3. Hence, it must have captured the missing Black rook. If that rook came from a8, the pawn formation means Black's king must have moved to let it out. And if the rook came from h8, castling would be doubly illegal.

But wait--isn't there a loophole here? Consider this sequence:

1) White plays g3 and Bg2
2) Black's h-pawn advances to h3, captures Bg2, and promotes to a knight on g1.
3) Promoted knight moves to e2 and c3, where it is captured.
4) Black QB moves to a6-d3-h7-g8
5) White h-pawn moves to h7, captures Bg8, and promotes to a knight.
6) White's promoted knight checks on f6, and is captured by Black's e-pawn.

Now the position in the diagram can be reached with Black still able to castle. Right? Wrong!

Remember, to set this all up, White's g-pawn had to move to g3 so Black's h-pawn could bypass it and capture on g2. All this happened before White played dxc3, freeing his QB to move.

So how did that bishop get to h2?

If you've got the mind for it, retrograde analysis can spoil real chess for you.