"Achieve World Peace" is the name of an achievement given by Toadette in Super Mario Odyssey. The achievement includes finishing the "story" of each kingdom with the required amount of moons to make the Odyssey move to the next kingdom. The goal of a World Peace speedrun is to beat the game as quickly as possible while completing all the requirements for the achievement. Timing for the run begins when selecting "Start" on a new file and ends when shooting out of the electric wire in the escape sequence.
The Any% route already achieves peace in 7 of the 14 kingdoms, so World Peace is a sort of variation on the Any% route.
The World Peace route is 100% modular, meaning nothing in a kingdom influences anything later in the run.
The document for World Peace only includes the altered routes from Any% (Routes for Sand, Lake, Wooded, Metro, Snow, Seaside and Luncheon)
This tutorial series by Tomshiii focuses on the differences compared to the Any% route and is a great way to get started in this category.