Each island is an old year.
5 seconds sound clip from the Rudolph's Shiny New Year movie soundboard.
You can hear this line at 00:14:00 in the Blu-ray version of the movie.
Quote context
[...]
- Do you have any idea where he went?
- His nurse, Nanny Nine O'clock said that he always wanted to see the Archipelago of Last Years.
- What does that word mean, sir?
- It's a group of islands. The Archipelago of Last Years is the most fantastic archipelago of all.
- Time stands still, and remains just the same as it was during the year he reigned.
- The Archipelago of Last Years.
- Happy may be hiding on one of those islands. On one of those long ago years.
[...]