This is a matter of knowing versus comprehension. It's also a matter of practicality. Yeltsin could have undoubtedly found out the contents of the average American grocery had he cared to. It's doubtful the United States would have exerted much effort to stop him from discovering Pudding Pops or Coca-Cola. But Yeltsin never had any reason to. It was simply never relevant. Do you think Donald Trump or Obama have ever shopped in a Chinese supermarket? Probably not. It's just not relevant to their lives.

Yeltsin also probably had statistics on standards of living available to him. But it's another thing to actually see and experience it. In addition, coming from the Soviet world where statistics were often... dubious if not outright fabricated, he had at least some reason to be suspicious.

Now, onto the context. What is not open for debate: Yeltsin did indeed visit an American grocery store. He had, by all reports, a grand time. He tried some of the wares and the manager gave him some free food to take with him. He inquired about the food distribution system and how managers were chosen. He was deeply affected by this and repeatedly commented on how much better the standards of living in the US were, both to people there and to his aides. Likewise, Yeltsin' assessment that the United States was wealthier and did a better job providing for its people was simply objectively correct. There is some controversy on this point by Soviet apologists, but I'm not aware of any mainstream historian who disagrees. (There are reasons for this other than Communism, but this does not change the standards of living themselves.)

All this is attested to by multiple sources who tell the same broad story with only a few minor contradictions or unverified reports. One aide, for example, recalls Yeltsin planned to open his own chain of grocery stores on this model, and spoke about grocery stores as the fundament of the modern world. While this is not mentioned in other reports, it doesn't really introduce ambiguity into the narrative. It broadly agrees with the other accounts and doesn't contradict them in a meaningful way.

But let's pull back a little. Because this incident didn't come out of nowhere. The Soviet Union and the United States had been competing on the standards of living for decades, going back to the '50s. Before Yeltsin visited the supermarket there were multiple incidents like the Kitchen Debates and other displays where both sides tried to outdo each other in living standards. In reality, the United States was always ahead but the Soviet Union was willing to lie to make it seem otherwise. From time to time, someone would expose this and embarrass the Soviets.

By making a surprise visit and comparing conditions, Yeltsin was acting in a tradition that would have been familiar both at home and in the United States. The surprise was that Yeltsin openly admitted his side wasn't winning. That had never happened before.

Why did he do that? Well, he says in part because it was true. And it certainly was true. But, and I have no citation for this, politicians lie. And (I do have a citation for this) the Soviets lied all the time to make themselves look better. Why the reversal?

The pat little story is that Yeltsin saw this grocery store and decided to fight Communism. This has no historical evidence: the reforms began in 1986 (three years before) and Gorbachev explicitly wanted to preserve Communism. Yeltsin was a critic but was not, at the time, explicitly anti-communist. The context was instead of a world where Gorbachev was trying to thaw relations with the United States and reform/revitalize the Soviet Union. He was a reformer doing battle with hardliners at home while trying to keep liberals from tearing the Soviet Union apart. And Yeltsin was a reformer.

By losing one of these 'kitchen debates' (for lack of a better term) he was damaging the conservatives who didn't want to admit the Soviet Union was behind while encouraging his own reformists. It was an attempt to show he was willing to break with previous policy and tradition to force the Soviet system to be examined and reformed. At the same time, hardliners would be put in the awkward position of having to lie without the support of the Soviet government (as a result of Gorbachev's reforms). And without that support, their lies would be much more apparent. It would also warm relations with the west at a time when the Soviet Union was vulnerable (and where Gorbachev was trying to warm the relations).

But none of this answers the more personal question. This is more an explanation of why friendliness to the West fit well into his general program. Why did the visit affect him like this? Yeltsin undoubtedly had more power, prestige, and luxuries than anyone else in that store.

In short, because Yeltsin was a Soviet.

It's easy to dismiss people with different belief systems as either secretly believing what we believe or believing in some more base philosophy. For example, saying that Stalin's actions were not really about Communism but about power. No one could really believe that, could they? Well, usually, yes. They could and did. And Yeltsin's autobiography shows that he really, truly believed in Communism. But he believed it in a specific way: he believed it was right, that it was better for the working class. And this was blatant, empirical proof that the United States was beating them in providing for the working class. This is what he tells us himself.

And that genuinely shocked him.

Sources:

• Leon Aron, Yeltsin: A Revolutionary Life (St. Martin's Press, 2000).
• Mohr, Charles (25 July 1984). "Remembrances of the Great 'Kitchen Debate'". New York Times.
• Yeltsin, Boris. Against the Grain. London: Jonathan Cape, 1990.
• Shevtsova, Lilia. Yeltsin's Russia: Myths and Reality. Washington: Carnegie Endowment for International Peace, 1999.
• And of course the news article on the event: http://www.chron.com/neighborhood/bayarea/news/article/When-Boris-Yeltsin-went-grocery-shopping-in-Clear-5759129.php

Edit: Thank you everyone for the great response! I've edited a few grammar mistakes.

There's definitely more to be said here, but I hope in the meantime you'll check out /u/Skiosmagus' earlier answer:

• I've heard that Yeltsin was famously shocked by the luxury of a typical American supermarket? What are the historical facts behind this story?

Skiosmagus does quite a nice job contextualizing the anecdote and how it has become mythologized in the USSR's own self-image. It would be really great if we had someone come along who could contextualize Yeltsin's own account of it in his autobiography (how trustworthy is he? what images of himself, the USSR, and Russia was he using his life narrative to project? &c).

ETA: People are saying the above link doesn't work on mobile; it's fine on my laptop (Windows/Chrome). Here's the straight-up URL: https://www.reddit.com/r/AskHistorians/comments/6kh3dw/ive_heard_that_yeltsin_was_famously_shocked_by/

For /u/Falco4Real, /u/litsax, /u/ReniePenie

I read a non-academic book a couple decades ago that said that Soviets consumed more of every class of food (grain, dairy, fruit, vegetables, etc.), except meat, than Americans. Can anyone comment on that? I'm not sure when it was referring to, though.

Edit: put it up as its own post here.

Update: no, it is not true. Americans ate more of everything but grain/potatoes.