There are two versions of en. (It sounds like you know the following, but just to be clear…)

One is a preposition. This usually means "in" or "while" (but can mean several other things).

The other is a pronoun. This replaces "de ____", so it could be translated "of it", "of them".

Il reste quelques biscuits. J’en ai mangé trois. (I ate three of them)

If you were to leave off the number, we’d get English "I ate some (of them)".

As-tu essayé les biscuits ? Paul en a mangé (he ate some of them), et il dit qu’ils sont bons.

Now for your world sentence. Suppose we drop en: you’d still have un "one", but you’d have to ask: one what?

This is what en does as a pronoun. It gives us the implicit un (des mondes). "One what? One world."

Ben points out in the comment that you could also repeat the main noun itself:

Un monde sans danseurs n’est pas un monde.

Also, I didn’t think about this before, but you could leave out en and have it just mean "A world without dansers isn’t one" — isn’t unified and whole. But that’s not what you mean, of course 🙂

Let’s take your sentence, made more explicit :

Un monde sans danseurs n’est pas un monde.

Let’s avoid repetition by using en :

un monde sans danseurs n’en est pas un. [de monde]

Though less common with être, the logic is similar to the classic construction with avoir :

Combien ai-je de frères ? J’ai un frère.

Let’s avoid the repetition by using en :

Combien ai-je de frères ? J’en ai un. [de frère]