White Night is a "theme" for one of the nights on the cruise. I've only be on one New Crystal cruise, so I'm not sure whether they have one every cruise, but I get the impression that they do. So, everyone who participates wears white, or as close as white as you have with you. I was told that my St. John white and navy striped skirt set was "close enough" to white. The ambassador hosts wore white shirts and black pants. The ship officers were in Dress Whites. I saw one older couple getting their photograph taken, she in what looks like might have been her wedding gown; very sweet.
So, after dinner, the party is in the Crystal Plaza. They put on a bit of a floor show with the cruise headliners (female singer, male singer, violinist, and dance pros). They were serving passed hors d'oeuvres. They then opened the Plaza up for dancing - it was a nice dance floor. I got to dance three songs with the dance pro. People who didn't dance lined the balcony on Deck 6 to observe. It was fun.
My impression was iff you didn't want to participate, or didn't pack something white, no worries. The dining venues didn't care what you wore. And you could just choose not to go to the Crystal Plaza that night. Or hang out on Deck 6 near the Bistro and observe the festivities.