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I'd like to understand how and why this stuff is useful for programmers.

Watch his lecture series on YouTube. We you started programming, you had to adapt your brain to the way of thinking of computer programs. Think of this as an continuation of that evolution, were you acquire new methods of reasoning that can abstract many apparently different problems into the same concept.

Is it only applicable in e.g. Haskell, though, or is it language agnostic? Thanks for your answer.

In a different comment thread, someone mentioned the book, Category Theory for Programmers. Here's the Releases page with PDF files (click to open the Assets section). https://github.com/hmemcpy/milewski-ctfp-pdf/releases

There are several versions with code examples in Haskell, OCaml, ReasonML, and Scala. These are all typically associated with functional programming and category theory. However, category theory is a much wider and deeper subject than any specific language, and deals with mathematical objects and concepts relevant to (more or less) all of programming.

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