It’s inversion. Instead of saying Les enfants lisent quoi (the normal subject-verb-object word order), the subject and verb have changed places, and the object precedes them. And then, because quoi is used only after a verb, it reverts back to its “normal” form que as an interrogative pronoun.

Building inversion

lkl’s answer is right about inversion. I however find his answer about when you can use inversion unclear, so I’ll complete here.

First off, inversion is a more compact form, but using est-ce is the standard in spoken language. First off, how is it built:

Qu’est-ce que les enfants lisent ?
Que lisent les enfants ?

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Qu’est-ce que c’est ?
Qu‘est-ce ?

As you can see, you can:

• either use the affirmative structure, preceding it with qu’est-ce que;
• or use only que and move the verb before the subject.

This is applicable only when que is not the subject of the question.

When the interrogative pronoun is subject: no inversion

Qui est-ce qui achète ces pommes ?
Qui achète ces pommes ?

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Qui est-ce qui a fait ça ?
Qui a fait ça ?

There is no inversion here.

You can remove the est-ce qui in this case. The intonation becomes important here, since there is no difference between the question and an affirmative subordinate clause.

There is some similarity with the other answer I gave you about how to choose the pronoun (qui/que) according to whether it is subject or not.

Other pronouns

I can’t think of a structure using another pronoun than qui and que which could lead to this kind of construction duality. This is deeply linked with the qu* est-ce qu*, which works only with qui and que.