Bitcoin mining, WTF?

I came across the term "bitcoin mining" in a NY Times article... which didn't bother to even hint at what that meant, apparently assuming everyone knows. So looked it up in some reasonably reliable fact resources on the net, including wikipedia, having to learn the word "blockchain" to understand it. But I am left with a serious question to which I cannot fathom a reasonable answer. It is this: why on Earth would anyone assign any value to this nonsense and why do cryptocurrencies have any value whatsoever, since they apparently have nothing to do with any kind of useful production or even information? The factual accounts I read give no hint of any kind of sensible answer to my questions.