After taking damage from an enemy champion, the next 3 spells or attacks you receive deal less damage.
Conqueror's ramping damage in extended duels is perfect for Jax's auto-attack based fight pattern, allowing you to pump out massive damage over time.
Jax is a solid tower diver and Triumph's big heal can make the difference between life and deal in sticky situations.
All of Jax's damage comes from his ability to auto attack repeatedly and Alacrity helps your early game trades and skirmishes massively before you're able to build any significant Attack Speed. It also allows you to opt into more defensive items so you can prolong the trade.
WhyCoup De Grace
Your rune choice here largely depends on if your laning against a tank or not. Coup De Grace is good at killing squishy champions.
If you are laning against a tank, take Cut Down.
Chrysalis' early game health allows you to take aggressive trades with Conqueror to get a lead and once you've converted the health to AD, you'll have the damage to split push without contest.
Bone Plating patches up some of Jax's early game weak laning power when trying to enduring any harassment.