How does the sixty-move rule affect the endgame?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
It forces the stronger side to make real progress rather than drift. After sixty moves without a capture, a game is adjudicated a draw, which means a player who is technically winning still has to actually convert the position: aimless checks and pointless piece shuffles are not enough, however comfortable the material advantage looks.
Why it rarely matters with correct technique
Any basic mate, played accurately, takes a handful of moves, well inside the count. The rule only becomes a real danger when a player has forgotten the technique and is genuinely just checking the general around without a plan, hoping something turns up.
What counts as progress
Only a capture resets the count, but the rule is really a proxy for whether you know what you are doing. If you cannot see how your moves are approaching mate, that is the real problem, and the counter is simply where it becomes visible.
Related questions
Does check reset the count?
No. Under the WXF rule only a capture resets it; checks and soldier moves do not. A string of checks with no capture keeps the counter running.
What happens at sixty moves exactly?
The game is adjudicated a draw. See how to avoid throwing a won endgame away with repetition for the related perpetual-check case.