Audio Return Channel is the means by which your amplifier is supposed to accept audio from your TV for playback, when the audio is sourced by either the TV, from such things as broadcast, cable or satellite, or in your case, Blu-ray playback. (tongue-in-cheek) It is needed because, Hollywood in the USA considers all analog audio to be copy-able by pirates, so all content they release needs to be encrypted to prevent such a thing, so end-to-end encryption is required meaning, every device has to pass a digital signal, and that signal needs to be encrypted. Analog sources aren't so easily encrypted, so they are usually just blocked.
From my understanding, it can happen either through the same HDMI that feeds signal from your amp to your TV, or it works through a separate connection from your TV to your amp, if you do not connect the device supplying audio through your amplifier.
If you are not connecting your amplifier to either your Blu-ray player via HDMI, or to your TV's audio return channel HDMI port via HDMI, I wouldn't expect your amplifier to give you any sound. It's an unfortunate side-effect of Hollywood's obsession with piracy.