I always love the scenes where Gibbs calls Ziva, 'Ziver', so this is my interpretation of how it came about and its significance.
Ziver. The first time he said it he had not really meant to say it, it had just slipped out, but he hadn't corrected himself because it felt right in the way it had rolled off his tongue, sounded right in the way the word fell from his lips.
Ziver. That first time it barely even registers with her. She assumed he made a mistake and didn't think about it again. Until the next time he said it.
Ziver. The second time it is deliberate but it still sounds as sweet and right as before and he smiles slightly.
Ziver. She stops for a second in surprise. Once is a mistake, twice is becoming coincidental and if there is one thing she has learnt in her time in America it is that you should not believe in coincidences.
Ziver. It is becoming a habit for him to use this nickname when he wants her to listen.
Ziver. She smiles softly as she hears the term of endearment. She's never been given an affectionate nickname like that before and she finds that she likes it.
Ziver. He doesn't say anything about it and neither does she but soon he finds himself using it often and it comes to mean a lot.
Ziver. It can mean "cut it out."
Ziver. It can mean "what's wrong?"
Ziver. It can mean "I'm here for you."
But most of all, Ziver means, "I love you."