What is 'real socialism'?

To answer the three questions from the OP in a tl/dr way:

where does the term come from (who invented it and when)

Terms like "real socialism", "actually existing socialism" etc were used by official quarters of the Soviet Union and its satellites from the early 1970s on. E.g. "real existierender Sozialismus" in 1974 by Erich Honecker (East Germany), according to German Wikipedia. But the article also states that this term (or similar ones) had been in circulation for some years by the time of Honecker's speech.

what is its 'official' meaning

The official meaning is something like "socialism in practice". I.e. not the utopian socialism or communism described in Marx' works, but something that comes very close and has been/ can be realistically achieved. I would argue that the meaning of the German word "real" is not exactly the same as that of the English word "real". E.g. you can not really use it as a synonym for "genuine". cf Realpolitik. No idea about other relevant languages though.

and what does it, from the popular perspective, mean?

Not sure about the 70s and 80s and other countries, but in current German usage "realexistierender Sozialismus" is a generic and commonly used term to allude to the general situation in East Germany from roughly 1975 to 1989.

What kind of socialism is "real"?
Socialism is a poorly defined term, that is often misused and abused in a political discorse. Thus, claiming that any kind of socialism is real to the detriment of other kinds, prejudges the discussion.

Without intending to be comprehensive, let me point out a few aspects of what socialism may refer to:

• Variety of political movements that arose in the XIXth century in response to liberalism. Liberalism puts in the center the individual and the individual rights, whereas socialism prioritizes, at least to some extent, the common good over the individual. This is vary vague and there are singificant differences in interpretation between different countries, social movements, etc.
• Socialism in the communist doctrine, as described by Marx, Lenin and their followers, is the transition stage between the imperialism (the last stage of capitalism) and the communism. In particular, all the countries of the Soviet block officially referred to themselves as socialist - the communism being only the future goal, but not the current state of affairs. In economic terms most of the property belonged to the state, which also controlled all the commercial transactions, prices, etc.
• Social democracy is the economical system existing in many European countries, such as Sweden, France, Germany, etc. It is essentially a capitalist system, where significant part of wealth is redistributed to reduce the economic inequality ("from rich to poor"). While colloquially it is often referred to as socialism, none of these countries officially uses this term (to my knowledge).
• In many countries there exist socialist parties, which has either history going back to the XIXth century, or which are simply former communist parties that have moderated their stance.
• Finally, the word is frequently used without any specific historical, political or economical ideas behind it, simply because all the things social are viewed as good in comparison to all the things individual/selfish/capitalist.

Developed socialism
If we base our discussion on the Wikipedia link provided in the OP, then real socialism is actually poor rendering of the Russian term that is more literally translated as developed socialism. Although the expression real socialism might have been used alongside it, and waq probably the equivalent term in languages other than Russian, it misses the original intent of the term.

Meaning in the context of Marxism-Leninism
Marxist-Leninist philosophy interprets history as an evolution of economical relations, passing through clearly defined stages of primitive society, slavery, serfdom, capitalism, and communism. Every stage is considered as more progressive than the previous one, and is itself subdivided in sub-stages, corresponding to its growth, maturation and eventually becoming outdated - at which point it delays the development of the society and must be replaced by a more progressive stage in a course of a revolution ("necessarily violent", according to Marx). Thus, developed capitalism also means mature capitalism - a stage where the progerssive aspects of capitalism in comparison to serfdom have been fully developed, and we approach to its collapse. Developed socialism was equally supposed to mean mature socialism - a stage which had to be followed by the inevitable rise of the communism.

Developed socialism in practice
While the substages of capitalism were well classified, the transition to communism was less clear. In fact, it was originally believed that communism was to immediately follow the collapse of the capitalism, and the forced redistribution of food and goods period of the civil war that followed the Great October Socialist Revolution was referred to as military communism.

However, the inadequacy of such a view became quickly obvious, and socialism was philosophized as a transition stage between the capitalism and the communism, where the private property still exists, and the society is not yet fully classless. In fact, the liberal New Economic Policy introduced by Lenin in the aftermath of the civil war was soon followed by another attempt at forcing communism, known as Collectivisation, which soon failed and was blamed by Stalin on the excesses by local authorities.

After Stalin's death, the inability to attain communism could not be blamed anymore on the internal an external enemies, which led to proliferation of slogans such as this generation will live under the communism, later replaced by our children will live under the communism. As in Brezhnev years USSR entered the period of economic stagnation, a more elaborate theory of socialism was developed, where the socialism was made in a separate stage of social development, alongside capitalism and communism, and its ongoing sub-stage was called developed socialism. Thus

• One could justify why building the communism was taking so long
• The current economic state could be presented as an achievement (after all, we have reached the developed stage)
• It held the promise of communism coming soon

Using term developed socialism instead of real socialism allows quickly to identify relevant resources, such as this article.