This is the 7283rd most frequent Russian word.
всемирному
"Всемирному" means "to the worldwide" or "to the universal," depending on context.
In this sentence, "всемирному" is used as an adjective meaning "worldwide," agreeing in gender, number, and case with "движению" which is dative singular.
Всемирному движению за мир нужно наше поддержание.
The worldwide movement for peace needs our support.
Here, "всемирному" modifies "уровню," highlighting a worldwide scope and is in the dative singular form to match "уровню."
Мы должны уделить внимание всемирному уровню образования.
We must focus attention on the global standard of education.
"Всемирному" describes "сотрудничеству" in the dative singular, emphasizing global integration or partnership.