The key idea here is to sacrifice the rook to get a queen and transpose into an easy queen vs rook endgame. White must prevent Black’s king from imprisoning the king in the corner at all cost lest the game is drawn (that’s also why the Black king needs to be at least four files away from the action in order for White to win). If Black moves Kd7 instead of Kd6, the win is even easier: 1. Rb8 Ra2 2. Kb7 Rb2+ 3. Ka6 Ra2+ 4. Kb6 Rb2+ 5. Kc5! and the marches down the b/c file until he reaches the rook. Source: Jeremy Silman’s Complete Endgame Course.
Note that if White’s rook could access b7 with check (if it was on h1 instead of e1, for example), White’s road to victory would be much more straight-forward, e.g. 1. Rh7+ Ke6 2. Rb7 and there’s nothing Black can do to prevent Kb8 and a8Q except to delay it with a couple of checks by playing Rh2 followed by Rh8+. The reason why the position of White’s rook at e1 requires the more elaborate ploy of the rook-sacrifice is because if he tries something else, say, 1. Rh1, Black can approach with his king, 1. … Ke6 and after 2. Rh7 Kd6! 3. Rb7, Black has 3. … Rh2! and it’s a draw because the White king can’t move (4. Kb8?? Rh8#) and rook moves lead to nothing (4. Ra2 Kc6 5. Rb3 Rh8+ 6. Rb8 Rh3 etc.).