Now, as far as what the word means then its good to recognize it has the word 'ai' in it so it is something related to harmony. Ma means space. Maintaining a harmonious space.
For starters I am not knowledgeable of the Japanese language and I am not saying the following comment is a definition for ma-ai. My comment is related to the original topic of distance and body structure but looking at the above thought from a diffferent persepctive.
For seconds when I trained Aikido my understanding of ma-ai was very similar to the posts so far on this thread. As I have trained in another art for the last many years my views and understanding have changed, grown, whatever you want to call it. I am not saying my previous views were wrong, I am saying my current views are much broader.
The quote above has 'ai' as harmony and 'ma' as space but the final definition adds the extra word of 'maintaining' which alters or limits the definition. Perhaps in a manner that was never intended?
Remove the word maintaining, and you get space harmony or harmony with space. Think about this for awhile, the concept of the principle becomes much deeper than simply maintaining a predetermined distance or spacing.
The principle becomes finding harmony in any space.
To my current way of thinking that is far more valuable than trying to maintain a specific predetermined distance that in reality is rarely if ever possible outside the dojo. Ambush attacks, multiple attackers, grapplers, weapons, environmental factors (such as walls, stairs, cars, furniture, etc) are a reality that making maintaining a set distance/range unlikely at best.
Seems to me training to be in harmony or comfortable in all ranges is far more valuable and powerful than training to maintain a specific range that is unlikely outside the dojo.
As I write this it occurs to me that many of the terms used in Aikido have 'ai' / harmony as part of the concept and yet we tend to focus on what preceeds or follows the 'ai' more 'ai' itself. With the repitition of 'ai' perhaps the training focus should be on the harmony.
This is actually the direction of my own training the last many years, although we use simpler words like 'relax' 'calm' and 'comfortable'. Initially everyone focuses on the physical aspects of these words but the power is really on the inside. Being truly relaxed or comfortable has little to nothing to do with the physical body. When truly relaxed the body will tend to reflect what is going on inside but it does not always need to be so.
Learning to identify our own discomfort or tension and then learning to release/correct these states is tremendously powerful, for when we are truly relaxed we see opportunity everywhere we look. I.E. harmony at all distances/spacing/range.
Food for thought: If you train a specific range/ma-ai all the time and believe this is the range that must be maintained to be in harmony, what happens to you inside when the real world provides a different range? Do you deal with the situation as is or do you struggle to get back to the 'correct' range before feeling comfortable enough to move forward? Through out the process what is the level of your harmony?
How to train this is a topic far to huge for a post.
In Systema the phrase that has come up recently is foundational or base training. While this has always been a large part of Systema Konstantin Komarov has done a great job of explaining it and providing training methods and understanding. Emmanuel Manolikakis has an oustanding video on the subject called 'Base Training'. Some of the best $25 I have ever spent. As with all Systema training it can easily be incorporated into existing training programs of other arts.
So back to the original question, how do changes in distance change the bodies posture/structure. I think the answer is so simple it is very difficult. As the distances change, find comfort/harmony within yourself and with those changes and work from there. Discomfort creates physical tension which the attacker can and will utilize against you. Discomfort creates phyiscal tension which makes it difficult to move properly. Discomfort creates mental/emotional tension which limits the ability to see opportunities to escape, move or counter attack.
Training the foundation makes everything else much, much easier.