Imagine there's a contest where you need to pick out the five cutest faces out of 100 dog and cat photographs. The contestants that guess the photographs that are the most popular win a prize.
You could choose based on your own opinion. Of course, cuteness is highly subjective, so the chance that your preferences align with the most popular preferences are small. Instead, you might think about what others are most likely to choose – are the other contestants mostly dog or cat people? You could take it down one more iteration – anticipating what others believe the average opinion to be: does the average contestant believe there are more dog-loving or cat-loving contestants? And so on to higher-order guesses.
Keynes was an economist known for his work on how we think about the government, spending, and inflation. He set up a similar scenario to explain the short term fluctuations of the stock market (do we care more about fundamental value or what others think?).
There's many Keynesian Beauty Contents going on right now in the startup ecosystem. Early stage venture capitalists not only have to pick winners, but winners that later stage investors will also pick with imperfect information. Picking technologies to build upon isn't just a matter of what you believe is the best, but what will become popular enough for others to use and contribute to.
Important caveat: the winners of Keynesian Beauty Contests are rarely the winners in the long run (but how long is the long run?).