Fiora's Lore
I have come to kill you for the sake of honor. And though you possess none, you will die just the same.''
The most feared duelist in all of Valoran, Fiora is as renowned for her indomitable will and haughty pride as she is for her skill with the blade. She was born to Demacia's House Laurent, a once-proud family whose reputation was tarnished by the actions of her father. In an unprecedented move, Fiora challenged him to single combat and, upon winning, took control of House Laurent. Defying the Demacian establishment, she has set about restoring the reputation and pride of her family name, one duel at a time.
Through reading her lore, you can gather that Fiora is very a very cocky individual. She's the best and she knows she's the best - now she want's to prove to everyone else that she is the best.
Whever Fiora challenges you to a duel with Grand Challenge, it's her way of saying , " I Can beat you, and I know I can." Fiora sets herself one of two goals;
1) Proving to others she can kill them at a whim, or
2) Proving to others she's the most skilled and best at her art.
Once she has achieved her goal (winning a duel or out-manoeuvring them in battle), she's ready to prove herself in another duel. Allies and onlookers watching the duel, have just witnessed, Fiora, prove to them she's a talented and skilled duellist. The healing aura effecting them could be a sense of, 'Renewed vigour' " Fiora really is a talented duellist, I think we can win." Enemies are people who witnessed the duel and hope to see her fail. The healing aura could be seen as a 'Demoralizing' debuff on them. They either no longer want to fight, or simply know it would be futile to duel with someone as skilled as Fiora.
In a gameplay sense, this sense of accomplishment is hard to convey. How do you tell someone is cocky and deserving of their title?
You can't just;
Otherwise failing to gain those benefits after using her ultimate, you'll feel hard done by. Fiora as a character is confident. If she wins, she won. If she loses, you were dishonourable and never accepted her challenge.