The endurance attribute affects the game through the Fatigue system. Each player starts the game on 0% fatigue, but participating in contests raises it, plus getting a Knock as part of a contest raises it even more. The amount of fatigue from being the attacker in a contest is 0-4%. The amount of fatigue from being the defender in a contest is 0-2%.
Participating in junktime adds a flat 1% to fatigue. Junktime happens between certain plays to simulate a chain of uncontested possessions, and its participants are completely randomised based on the ticket system (without attribute and skill bonuses).