What specifically are you confused about?
A Player Action Window is simply the point in the game where players are allowed to use non-Response triggered effects. You know, event cards or other card abilities that have a phase name or "Any Phase" in bold at the beginning of it. So the "player actions aspect of the challenge phase" is just when during a challenge you can use an effect that starts with "Challenges" or "Any Phase."
If it helps, think of the "anatomy of a challenge" described above as:
1. Attacker names the challenge type and kneels attacking characters.
---> Players get to "do stuff."
2. Attacker assigns stealth, then defender kneels defending characters.
---> Players get to "do stuff."
3. Resolve the challenge.