"Achieve World Peace" is the name of an achievement given by Toadette. This achievement is the basic definition of the category. Achieving World Peace as quickly as possible. This roughly implies finishing the "story" of each kingdom with the required amount of moons to make the Odyssey move to the next kingdom.
The Any% route already achieves peace in 7 of the 14 Kingdoms. So the World Peace route is sort of a variation on the Any% route.
The world peace route is a 100% modular, meaning nothing in a kingdom can influence something later in the run.
The document for world peace only includes the altered routes from any% (So the routes for Sand, Lake, Wooded, Metro, Snow, Seaside and Luncheon)
This tutorial series by Tomshiii also focuses on the differences compared to the any% route and is a great way to get started in this category.