Why did Samoa skip a day?

Samoa didn't skip a day, it jumped forward a day.

To keep in sync with their major trading partners such as New Zealand and Australia, a decision was made for the day change.

Western Samoa crossed the International Date Line from December 29, 1892, straight to January 1, 1900. By doing so, they were able to skip the days, 30 and 31 December 1892. That's why you won't find any official records for those two dates in Samoa.