I know embarrassingly little about this, so my apologies if the time period is too broad. If it is, please feel free to answer for a narrower period of time!
I'll try giving it a shot, but maybe someone else can chime in with a better knowledge of Meiji period Japan and/or someone with a Cuisine flair. (If such exist). Also excuse me for grammatical errors, not a native speaker.
At the beginning of the Meiji Period the Emperor decided that Japan should embrace western influences, this would mean progress for Japan. Now this decision to embrace the West was a beginning of a lot of changes. One of these changes was lifting the ban on the ban of red meat. Before the Meiji period Japanese dishes were mainly rice and fish. When the Portuguese and the Dutch introduced fried food, the Japanese diet changed again to dishes like Tempura. Which did not replace but was added to the Japanese kitchen.
Now the eating of meat was a brand new thing! Imagine thousand year of vegetarian cuisine! Japan always had the Buddhist practice of not eating meat, I don't know anything about Buddhism. Only that Buddhist refrained from killing animals.
The Emperor of Japan held a New Year's feast in 1872 to embrace the Western World and people were eating meat in public. Meat is a consistent part of a European dish. Japan wanting to embrace this cuisine, created their own "Meat cuisine" called yōshoku. This simply means a Japanese style of western cooking. Incorporating things from Europe and mixing it with Japanese dishes. Before the Meiji period every food from another country was seen as yōshoku. That's why if you take a look at the dishes you see many from other countries varying from Russian to Dutch decent.
Japanese Curry, steak, spaghetti and so on. These things were getting more and more prominent. Also the croquettes and fried foods were not incorporated in the yōshoku cuisine. And these were in Japan since the 16th century and were of European origin (Portuguese mainly)
I can't really tell you anything about the change meat did to the inhabitants of Japan. It's a common saying that the Gaijin can't take the ordinary Japanese Dishes, because they're not used to such a diet. This also goes vice versa because Japanese people seem to get stomach aches from European food. (I read this in a book called Mizu shōbai where this is briefly mention, but I think it was more of a bragging conversation than anything else)
I recommend you to try the Fried foods they are delicious and if your a fish eater try it too, I'm not a fish eater really so I refrain from that. I recommend Tonkatsu which I could kill for!
Mainly sourced from The History and Culture of Japanese Food by Naomichi Ishige
And the New York Times article which Wikipedia uses.
Partially relevant, I recently answered a question about Japanese diets here in a HUGE writeup about the staples of Japanese crops and foodstuffs.
So before we go into the new stuff, let's review.
Japanese staples for the average citizen consists of:
As explos1v pointed out, due to Buddhism and Shintoism, there were certain times when bans on meat were in effect. But it was not a super permanent thing and was not a continuous stretch of time. For one thing, Buddhism's influence waxed and waned depending on the time period. Meat bans were also not in place universally across Japan as provinces enforced their own laws and rules. Finally, meat bans were lifted in times of famine, war, or otherwise times of hardship.
But even with all this, Japan does have a noticeable vegetarian tradition to their cuisine and culture.
The poor also had no qualms about eating meat to supplement their diets. Birds, rabbit, and deer were also eaten on occassion. Particularly mountain villages that had the least amount of arable land for farming had hunting traditions. They continued to eat meat.
Part of the reason meat consumption was so low was because of the aversion to raising animals to be slaughtered for food. Certain fowls were also co-opted into the Shinto religion as religious messengers and would only be raised to be 'criers' for religious ceremonies. Cows and oxen would only be raised in enough numbers as a work animal. Horses were strictly seen as a military/official service sort of animal.
Consequently, not only was meat consumption generally low, dairy products and eggs were also a rare sight at the dinner table.
Fish was still a very common dish though.
Now moving into modern times.
As xplos1v said, tempura was an idea that came from the Portuguese about 200 years prior to the Meiji Period. It caught on fairly quickly, by around the 18th century, so it was largely a part of Japanese cuisine by then.
The first big thing was definitely meat.
While meat consumption was not an alien concept to the Japanese, they were absolutely not used to eating it regularly. It's actually very pronounced in Japanese cuisine tradition because their cooking philosophy has a strong aversion to oily foods as well as a lack of traditional use of spices. Most of the spices that would have been consumed as a part of meat dish preparation was generally reserved for medicinal use only.
The really big change for the Japanese however was simply the tradition of raising large numbers of animals to be slaughtered in huge numbers if they were to consume meat at the same volume as Westerners. There simply was no parallel in Japanese farming. Many were opposed on various grounds from religious reasons, animal rights, to nationalism and conservatism.
But eating meat was very much the cool thing to do and it caught on very quickly, especially after the Imperial palace started a regular trend of having French style meals. The Emperor himself talked about how he liked the taste of good beef. Soon expensive, high class restaurants that served Western style meals popped up in major cities to serve the privileged, plenty match to a good restaurant in Paris. The more common folk adapted western style meals as well in a more casual way.
The next big things were consumption of dairy and eggs.
Drinking milk was never a big thing in Japan, or much of China or Korea for that matter either. It was seen as strange that anyone old enough to not be drinking from their mother's teat would willingly drink milk, and milk from an animal no less! Milk was something that babies and invalids drank because they had no choice, because they were unable to drink anything else.
Seeing Westerners drink milk by the glass was a big surprise. Opposition to it was high. Some would feel queasy drinking such a strong, fatty drink. Others refused to drink it on principle (as an analogy, how many Westerners would feel bad about eating a dog, a horse, or insects). Finally, some thought it just tasted plain bad.
But there was a large push for people to drink milk, part of the 'revolution from above', referring to the Meiji Revolution that the period is famous for. Drinking milk was seen as a part of a larger effort to adopt Westerner ways, which was really to feed into the larger goal of adopting the modernism that came with it, on a large scale with committed and sustained effort.
Cheese was just as hard to push on people ("who wants to eat rotten milk?? I don't even want to drink fresh milk!")
Eggs were more tolerable to the Japanese palette but still considered strange.
The final cuisine change that really rocked the Japanese psyche was the idea that rice was not the staple of a meal; bread was.
The Japanese were very reluctant to drop rice as their main carb. It's difficult to impart just how integral rice was to not just Japanese cuisine and farming but the very culture and way of life of Japan.
Rice was a measurement of wealth. It was collected as taxes. It could be used as payment. It was how salaries of soldiers were measured out for hundreds of years. Everyone ate rice if they could. It could be turned into liquor, cake, paste, soup. It was what connected the peasant to the emperor. It was part of religion. It was part of celebrating life, birth, marriage. It was the food offered to the dead and how families showed respect to venerated ancestors.
But with the flow of time and the flow of change, people got used to bread as well. It was soon not uncommon to see bakeries in major cities, though they often made bread that was more compatible with the Japanese sense of taste more often than traditional French or German bread, though those traditional bakeries were the first ones, mostly meant to serve resident expats, staffed by expats.
Another big thing was coffee. But Japanese people embraced coffee culture with a strong appreciation. Cafes were soon popping up and existed alongside tea houses.
This is the general summary of the largest dietary changes the Japanese experienced in the Meiji Period. The most important thing to take away from this is that the changes were almost exclusive to cities, and major trade cities at that. These changes rarely took strong hold in rural areas. For example, actual nation wide adoption of bread as a suitable substitute for rice just for breakfast, did not happen until the 1950s ~ 1960s. Meat consumption is the notable exception because the intense farming requirement involved spread the meat idea pretty fast.
Hope this answers your question! Cheers!