"Qu'aimez-vous?" means who or what?

Maarten and Jameson already explained that the "i" in qui never contracts. That's the reason you absolutely know that the first word in Qu'aimez-vous? must be que.

The next thing to keep in mind is the difference between qui/que as an interrogative pronoun (like in this sentence) and qui/que used as a relative pronoun.

Interrogative pronoun:
qui -- used for people ("who")
que -- used for objects ("what")

Qui vous aime ? -- Who loves you?
Qui aimez-vous ? -- Whom do you love?
Qu'aimez-vous ? -- What do you love?

Relative pronoun
qui -- used for people and objects as the subject of a relative clause ("who", "which", "that")
que -- used for people and objects as the direct or indirect object of a relative clause ("whom", "which", "that")

Je ne sais pas qui est venu. -- I don't know who came.
Je ne sais pas ce qui s'est passé. -- I don't know what happened.
Je connais cette personne, que tu m'as montrée. -- I know that person whom you showed me.
Je connais le livre que tu m'as montré. -- I know the book which you showed me.

Qui never contracts - see point towards end of lesson. Qui = Who/which/that (French Relative Pronouns)

Because QUI is never truncated. It is always QUI. So if you see qu'ils/qu'aimez IT IS alway QUE.