A/B comparison simply means that you play the same music on the same speaker at the same volume in 2 different scenarios. Sorry, it’s kind of an engineering thing, and because I’m an engineer, I presume that it’d be obvious to everybody, but apparently it’s not.
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Scenario A → listen to the music without the hearing aids on via the speaker. Note that we’re not talking about streaming music from a smart phone or whatever device to the hearing aids directly here. You’re playing music from whatever device you choose to the speaker, then you listen to how the music sound directly from the speaker, through the air to your ears.
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Scenario B → next, listen to the music with the hearing aids on. Preferably on the same song that you just listened to in scenario A. Does it sound better with the hearing aids on? Specifically, do you notice more high frequency sounds from the music? If yes, then as a sanity check, this is implying that your hearing aids is working and amplifying your hearing loss in the high frequency area and that’s why you can hear the music sound better in this scenario B.
You can switch back and forth between scenario A and B as many times as you like, maybe play different songs of different types, etc, until you’re sure that scenario B with the hearing aids on makes the music sound better. Specifically, it should be brighter, more treble, richer, fuller, and not dull like without the hearing aids.
The reason for trying to do this with music is that usually music is much richer than just speech or normal every day sounds. The normal every day sounds or speech may not have enough of the high frequency sounds that you can’t hear as well on, so in those cases, you can’t really tell whether the hearing aids are helping you that much or not because those normal sounds may dwell mostly in the low and mid frequency range where you don’t have a hearing loss. But with music, especially full and rich music, it should be much more obvious whether the hearing aids are amplifying the high frequency sounds in the music for you like it’s supposed to or not.