After that fight, the prince realized what was holding him back was that he was still human... he could still feel... he could still bleed. He still had a heart.
The first thing he did when he became king was to rid himself of it. He threw it down the pit where we first met. And you, <name>, were the first person to touch it since.
Notes
The duel
There are several stones scattered about the courtyard, just west of the quest giver.
Touching one the stones once again transforms the player into Arthas, with a different set of abilities. This time, it's a one on one with Illidan Stormrage: the same duel seen after the Warcraft III mission A Symphony of Frost and Flame. Arthas will start with 188,000 HP an an empty mana bar worth 25,014 MP. Illidan starts with 903,000 HP and Boss status.
Illidan Stormrage says: Prepare to die!
Arthas has four abilities:
1: Parry - "Parry Illidan's attack and regenerate 25% of your mana if successful." Makes Arthas parry Illidan's next attack, giving him mana, as he starts with none. Instant, 3 second cooldown.
2: Deathstrike - "Deal weapon damage +20000." A heroic strike for 20,000 Dmg, a mediocre amount of damage for this fight. 2000 Mana, Instant, 1 second coodown.
3: Stomp - "Knock Illidan back." Knock Illidan back, giving Arthas the range he requires to use Annihilate. 5000 Mana, Instant, 4 second cooldown.
4: Annihilate - "Leap at Illidan dealing weapon damage +400000 and stunning him for 6 seconds." A heroic leap attack that deals a substantial amount of damage, 400,000 Dmg, to Illidan. 10,000 Mana, 8-25 yard range, Instant, 15 second cooldown.
Parry until Arthas has enough mana to Stomp and immediately follow up with Annihilate. Do that about 4 or 5 times to defeat Illidan and complete the quest.
During the fight you will get a debuff called Pierced Heart. It's text is: Your heart has been grazed by Illidan's glaives. If only you could rid yourself of this useless thing...