Comparable to Magic: the Gathering's colors and Cardfight Vanguard's clans, the worlds divide the cards into groups based on mechanical and artistic themes, each world has its own artistic themes and playstyles, as well as a unique card frame that represent the world's theme (Example, Dragon World is themed after dragonic creatures, is focused on destroying opponent monsters, and its card frame resemble fire). Most worlds have at least 2 "main" attributes which can often be used to build decks for them using specific support for them (though those attributes don't necessarily have to be unique to said Worlds).
Each world is represented by a Flag card whose text determine which worlds you may use, because of that, it is recommended that your deck only includes cards from the worlds listed in your Flag card. However, you may include cards from worlds not listed in your flag, but they will be treated as "Blank Cards" with no information and cannot be played.
The Generic cards do not belong to any world, as such they can be used in any deck regardless of the Flag card.