This is the 470th most frequent Serbian word.
чему
"Чему" means "to what" or "what for" in English, depending on the context.
In this question, 'чему' is an interrogative pronoun in the dative case, asking for the purpose or use of 'овај уређај' ('this device').
Чему служи овај уређај?
What is this device used for?
Here, 'чему' is used as a relative pronoun in the dative case, connecting the verb 'питао' ('wondered') with the reasoning or purpose of the action 'читати толико књига' ('reading so many books').
Питао се чему читати толико књига.
He wondered what the purpose of reading so many books was.
In this sentence, 'чему' is again a relative pronoun in the dative case, referring to the abstract idea to which the subject's hope is directed.