Firstly, MQA attempts to deliver high-resolution audio with a smaller data size than it has in FLAC, without losing any fidelity. In theory this should be useful for streaming situations where bandwidth may be constrained.
In practice, the importance of consuming less bandwidth for home audio playback is pretty dubious in an era where streaming of HD video over broadband is common, which is much 'fatter'.
But does MQA succeed in making smaller files? Some question this, saying you can SRC FLAC to 18bits, equivalent resolution to MQA, and actually get smaller files.
Secondly, and more controversially, MQA claims to deliver better time domain performance by addressing "time smear", which is a reference to ringing associated with filters used in the DA conversion process. MQA claims this delivers better quality sound, although even they seem to be cautious about exactly how audible this is.
How important is this?
1. Pre- and post-ringing occurs in the vicinity of the cut-off filter, which for Redbook audio is 22khz.
2. Listening tests where subjects listen to different digital filters with different degrees of pre- and post-ringing have not shown a strong preference or even audibility
Which leads to:
Is MQA higher quality than a 24bit/96khz standard FLAC file? No, nor does it claim to be.
Does MQA playback pass a DBT ABX test where it is preferred vs standard Redbook with statistical confidence? I haven't heard of any DBT tests of MQA at all.