"Show don't tell," as a three-word directive, is pithy and simplistic. But it's used because it's one of the fundamentals of writing well, and one of the things new writers understand least.
As Lauren says,"showing" doesn't entail endless description of minutiae, or attempting to convey a cinematic level of visual detail using text alone. What is means is that reading a book is something you experience - and an author doesn't provide an experience by telling readers what to think or feel. You do it by showing -- by creating things that will provoke readers to thoughts and feelings in response.
You could reformulate this as "demonstrate, don't dictate." Saying Bob is a funny guy does not make the reader laugh. Saying Alice had a mysterious smile does little to convey mystery. Saying Grizelda was a very sympathetic protagonist, and then something very exciting happened to her is a very poor story indeed.
There is a lot of nuance to "show, don't tell," and it's certainly a guideline that can be misunderstood or abused. (The idea that you should "show, don't tell" for everything is a common misinterpretation; knowing what to show and why is an important skill.) But, this question isn't asking for a full explanation of "show, don't tell," it's asking why it's such popular advice.
And the answer is, because it's one of the major things beginners get wrong.
The art of writing is so much more than getting words out on the page, or transcribing the outline of a plot. It's the difference between having scenes, characters, and plot twists, that you're just assuming the reader will be willing to wade through -- and creating scenes that are vivid, characters you want to spend time with, plot twists that have real emotional impact. Beginner writers make this mistake all the time - they write something because "that's what happens in the story," but they forget to craft the way in which the reader will receive and experience it. This is the fundamental error: to assume that because the author has written it, the reader will experience it, believe it, enjoy it, in the way the author intended.
So "show, don't tell," when used correctly, is shorthand for "you have described this thing as a fact; you have described this event as occurring; but you have not made it interesting, emotional, intriguing, or impactful, in a place where you should have."
Another reason it's so popular is because it's kind of a catch-all for an emotional effect that's missing. Explaining that something is missing is generally tricky - it's hard to explain what is missing, and why it is necessary. But more to the point, other criticisms, which deal with something included which is done poorly, are simply much more direct -- so they never become pithy sayings.
"Brenda is a really boring character" or "I don't believe anybody would act this way" or "I saw that plot twist a mile off" or "This has been done a million times by better writers than you" are all common critiques for beginners too, but they're never going to become snappy aphorisms.
But, when the problem is not "This is wrong", but rather "something's missing," then you get a refrain that's in common use.
The point I'm making here is: "show don't tell" is hardly the only tool in writing teachers' arsenal; it just stands out disproportionately, because it's a single solution/guideline for many, many unrelated issues.
Obviously, "show, don't tell" is sometimes used incorrectly. And the fact that it's such popular, well-known advice makes it, well, better-known, more often discussed, and more frequently misused. But there is a strong core to the principle, and good reason for its popularity.