The first part - about the way the world had broken, about the people they lost by the hour every day - was difficult, and deeply shaming. Already, Leeloo had known that she'd needed to bring the Light of Creation to that world to redeem the rest of those who lived there. With Peter at her side, she could have done it at any time as the world continued to get worse and worse - could have done it and survived.
Then Peter was pulled away, and she lost the chance... But then, he explained that she'd done it anyway, that she'd fulfilled her mission (perhaps not in the way her people had expected her to, but still in a way that befit the circumstances), and that the world had been saved after all.
When Peter was done, she couldn't stop smiling. She knew, she knew that he was hurting from it, but she didn't have the words - not even in her own tongue - to explain the perfect rightness of what he'd relayed to her. She'd failed, she'd been failing - and then, when he finally left, she redeemed herself.
"Thank you," she finally said, that relief and redemption shining through the twist of syllables. "I will remember not to hesitate again, if I'm ever needed like that again."