It doesn't mean they are the world's best the next day, nor the world's best in history, but on that day, they hold the title. The world's fastest, the world's strongest, the world's highest.

Funnily enough, it is possible to be those things long after the end of the Olympics. You mentioned the Olympics, but you forgot about the world records. In a lot of the games, the participants are frequently compared to the WR, both to see how they stack up, and to know if a new record will be set. And for those that do set a world record, they are the best at that event in history, and in the future, until it is broken. Sure, that can be the best performance of their life, and their performance can weaken thereafter, but until that record is broken, their best performance is still the best in the world.

Since you mentioned being the world's best at random things, we also have Guinness' Book of World Records for that. You can check out the different and weird records there, and maybe you can find one where you can be the world's best at haha.