I have seen on many etiquette questions about Japan that this is a no no, but I can't seem to find what the reason for this is. I know that in countries like Taiwan or China it doesn't seem to be an issue at all, so I would like to know why there is such a difference.
Also, does this also apply to any public places, or just while moving around?
Since the issue is not only with food that you can spill but also with drinking from bottles or cans (even if you buy it from a vending machine, you are not supposed to drink it while you walk), which are not as easy to spill as walking around with a ramen bowl, this is not a hygiene issue.
The topic is much more about the respect for food at large. When Japanese people start eating, they put the hands together in a praying gesture and say "Itadakimasu", wich means "I humbly receive". People are also supposed to finish their food, even down to the last rice corn. There is another phrase to thank the cook once you are finished. Several other cultural details exist that underline this deep respect for food.
When you are eating while walking, you are taking food too casually, and forget to pay respect to the people who grew/made it and the souls of the organisms who perished in the process. You are supposed to cherish your food, which is taken to comical extremes in the "Ramen Scene" of the movie "Tampopo", which is a comedy only about food in Japan.
There are a lot of restaurants that serve food on the street, but you are supposed to eat it right there, on the spot, often under a canopy or umbrella, instead of walking away with it. Probably the only exception is ice cream. It is very possible that it is exempt because of western influence.
It's all about education. Kids are taught the following table manners from the age of around 2:
This is reinforced at kindergarten/elementary school lunches (no snacks, school-supplied lunch that's the same for every student).
Those manners stick.
And anyway, have you ever tried to walk while eating with a pair of chopsticks? You'll put your eye out!
I think more of it has to do with appearance than any sort of profundity everyone seems so fond of blaming. Japan is a HIGHLY image-conscious society, for better or worse, and stuffing your face while on the move isn't a good look, anywhere.
In regard to Japan having this religious respect for food, I don't think anyone who's been to a proper nomikai at an izakaya can say "japan doesn't waste food" with a straight face. I've seen heaps of great stuff NOT taken home in doggy bags because that would be "kakkowarui." And if it weren't the case, leaving the last bite of food for sake of looking like a greedy jerk wouldn't be so commonplace. People would be a lot more "mottainai."
Also, this stuff about japan being this "ultra-clean" society where they don't spill food on the street is rose-tinted idealism. A walk through central Shibuya on a early Sunday morning would not only reveal tons of wasted food discarded by local establishments, but also heaps of litter. Not to mention countless pools of vomit EVERYWHERE, planted for you by salaryman who couldn't hold their liquor the night before.
This isn't to say Japan isn't a deeply beautiful place with profound respect for all things, but I think a lot more boils down to trivialities than anything zen.
Don't limit your perception of japan to what you see in movies, TV, and your favorite new age bookstore. Sometimes a rice ball is just a rice ball. After all, "konbinis" don't exist because everyone believes in the sanctity of corn chips and "American dogs."
Of course, all this aside, despite the taboo against walk-munching, DRINKING (alcohol) in public (on trains, street, etc.) is fairly casual, particularly for men over 40. What about that, then?
When I brought this subject up to my Japanese hostess, she looked at me quizzically and pointed out all the locals doing just this and said it's fine and no one cares.
But this is in Tokyo, maybe somewhere less metropolitan they care more.
I assume it came from the zen buddhist philosophy. In spiritual life, You give utmost importance to every activity. You are supposed to do everything consiously including eating. Even in India where buddhism originated, it is generally not taken positively to eat while walking.
Fastidiousness. Being considerate to others.
As with many cultural peculiarities/quirks/anomalies, there is usually not one single explanation. But IMHO the single biggest explanation is a combination of being fastidious and considerate to others.
To walk while one eats or drinks is to elevate the risk of food/drink spillage. And doing any such thing would be truly awful because of the awful mess it would create and the awful inconvenience it would cause others.
The chosen answer suggests that if one buys food from a roadside stall, it is OK to stand there and eat it. This presumably shows adequate "respect for food".
But in that case, why is it not OK if I go to Lawson's, buy an onigiri, and eat it there? Wouldn't I be showing at least as much "respect for food" as in the above scenario?
The difference I think is that in the former case, it is customary and fully expected that the stall proprietors bear the burden of cleaning up after any mess that you may leave behind. Whereas in the case of Lawson's, it would be a terrible inconvenience that you'd be causing the already-busy employees were you to spill any food.
P.S. The chosen answer also claims that the Japanese "respect for food" is reflected in the way in which they eat every last morsel of their food. This has less to do with "respect for food" than with the historical experiences with deprivation.
The Japanese proverb 粒粒辛苦 ("every grain hard work") which every Japanese schoolchild is taught, comes directly from the Tang Chinese poem which every Chinese schoolchild is taught (谁知盘中餐,粒粒皆辛苦).
The point is NOT about any semi-mystical "respect for food". Instead it is simply about avoiding the waste of any food or any resources in general about not wasting food or resources in general (mottainai in Japan).
Thus, the Chinese, like the Japanese, eat every last morsel of food because in both cultures, one avoids wasting food or any resources. However, the Chinese, unlike the Japanese, are perfectly fine with eating/drinking while walking, because the Chinese are less fastidious/considerate than the Japanese and are less bothered by a bit of filth and disorder (as is evident once one spends a bit of time in each country).
P.P.S. hippietrail suggests in a comment that "people in Asian countries don't eat while walking generally". This is false. It is Japan and solely Japan that is anomalous in this regard. (Note that of course historically, pretty much EVERYWHERE in the world, people generally never ate while walking. It is mostly in the modern busy era that people do this. And only in Japan is there an unwritten prohibition against doing so.)
In Japan you will notice that outdoors or at other public places it is very clean, even in places with very few garbage cans. Traditionally Japanese are very clean and respectful of others. If you are eating while walking it is sometimes difficult not to make a mess or drop something.
Also there are so many restaurants that it is unnecessary to eat while walking about. It's little problem to get a good meal that you can eat quickly, near your work or wherever you are.
Just adding my two cents: In my experience, the reaction you get from Japanese when you eat something while walking is just a blank expression and a "Why?". And when you answer that with a "Well, why should I sit down for an Onigiri, they are practically made for eating while on the run", they just go "Hm, you're weird".
So my theory is that Japanese people don't do it because the idea simply does not enter their head. No one ever does it, so where should they get this weird idea from?
