MQA is a solution to a problem that may or may not be important. The basic premise behind it is that high resolution audio should be streamed but since there is not much signal above 20 Khz, in order to conserve bandwidth, the portion above 20 KHz can be separated out and delivered as a lossy signal.
Basically MQA delivers lossless audio up to 20 KHz but also takes the content above 20 KHz and encodes it a signal that it hides below the noise level. On playback, the high sample rate data is retrieved from the encoded data. The idea is that that high frequency content is small, so even an lossy representation of it is adequate to provide the high frequency content.
The theory is well developed and very sound given the premise. I think you would be hard pressed to hear the difference between the original high sample rate original and the MQA decoded result.
In addition, MQA provides specific information for the appropriate filters to be used by a DAC on playback.
So, the full MQ decoding process includes decoding the content back to a high sample rate and then further applying a final upscaling and filtering process based on the characteristics of the DAC. The first part can be do in software. The final process is specific to a particular DAC so it can only be done in hardware.
The MQA content will always be an incomplete representation of the original high sample rate data, but it is probably pretty close for most listeners. Whether it is equal or worse than than the original high sample rate file depends on the equipment being used and the ears of the listener.
One addition advantages of MQA is that most of the albums have been remastered in the process. So, even if you are only listening to the Redbook portion, the sound may well be better than other versions.
To Awesome Donkey's point, the developers of MQA have never claimed it is a toally lossless process. They do claim that the data below 20 KHz is basically lossless but they readily admit that the high sample rate data is lossy, based on their proprietary algorithms. I say basically, because the high frequency data is embedded below the noise floor. So, technically the base signal is not lossless, but for all practical purposes it is.
MQA is a proprietary process and is therefore criticized by many, simply because it is proprietary. It is meant to deliver high sample rate content in a smaller package. And, it is meant to optimize the filtering based on the specifics of the DAC. In doing that, it does exactly what is is meant to do. The question is whether any given listener can hear the difference.
As an example, Tidal takes a MQA file and decodes the high sample rate encoded data and assembles it into a high resolution signal. A MQA DAC can do the same decoding but also adds the upsampling and filtering designed for that DAC.
There are other nuances to the process, but those are the basics.
So, if you have access to Tidal or another MQA source and/or a MQA DAC, listen and decide for yourself. The remastering, independent of everything else, may be enough for your to hear an improvement over previous Redbook versions.