Lesson
White to move. Main line: 1. Ra8#
The white king on h6 does the quiet work: it takes g7 and h7 away from the black king. That leaves only the back rank — and Ra8 covers all of it at once.
This is the simplest mating pattern in chess: king restricts, rook delivers. Every rook ending you will ever win funnels toward this picture.
The kings stand in opposition here — same file, one square between them — and that is what makes a single rook move final. Put the white king on g5 instead and Ra8+ is only a check: the king steps to h7 and the chase starts again. Bring the king first, check second.