Joe, with all due respect, there is nothing to buy ... it is an accepted fact in the world of exercise and fitness ...
... others above have articulated the brains involvement, but my emphasis is on the muscle cell, and the bodies ability to repair/rebuild and adapt ...
... with that said, I will try to be brief ... any motion we make, recruits and actually destroys/damages muscle cells with that movement. With that premise accepted (its science) the body recognizes any repetitive/strenuous motion requires the damaged cells to be rebuilt stronger/more resilient than the previously damaged cell ... take a look at any NATURAL bodybuilder, and what they have accomplished with this process. Now along with the muscle repairing/rebuilding that is taking place, the connective tissue also being recruited (tendons/ligaments/insertions) adapt to the physical requirements placed on them, and they too adapt ...
Now if we fast forward in the cycle for sake of brevity in this explanation, our body adapts to a repetitive process such as the one described above, and actually adapts in its own way to perform the functions easier/more effectively, which in turn cause less damage to itself ... in othe words, our muscles (OK, our BODY ie: mind, muscles, etc., etc. if that fits better) actually 'remembers' what is expected of it (because of the repeated exposure), and adapts, to facilitate the challenge more efficiently ...
In my training consultations, I often use the example of the young apprentice roofer who has trouble walking along a steeply pitched roof ... well, after he has been at it for years, his body has adapted to the point that his MUSCLES, joints, connective tissue, etc makes the adaption to allow him to walk effortlessy for hours on end on steep pitches ...
The term 'muscle memory' may not be accurate in all cases that these bodily adaptions and transitions take place, but 'muscle memory' is a very real and relatable term that is well understood in the world of kineseological studies ... and it only makes sense that it would also be relative and accurate to describe the process taking place in the hands, which happen to involve some of the most delicate of all components in the human body .... JMHO, but it comes with years of seeing it happen first hand in the real world ... I have seen fitness competitors that have not trained for years, sometimes even decades, make comebacks and very quickly return to the point that they were at when then quit ... many, many times quicker than it originally took them to make those gains ... and THAT, is directly related to the term we use in the industry as "muscle memory' (the muscles 'remember' the repititions from previous exposure, and adapt quicker) ... if someone has a better name for it, that is fine, but you will get a 'deer in the headlight look' when you use it, as 'muscle memory' is the accepted term to explain it ... 'muscle adaption' may be more accurate, but 'muscle memory' is one of the generalizations used to describe the process, which obviously recruits more than just muscles ...
hopefully now the process makes more sense ... and of course the muscles would not be able to perform any functions by themself without the brain and central nervous system, etc. to ochestrate that movement, but with enough repitition and adaption, it really does almost seem it is an unconcious movement when we are playing riffs at times, doesn't it? ... Rumblefish above describes the process in terms that I dont even attempt to understand, but I have seen it demonstrated daily for years, whatever you want to call it
