At a concrete use case level, it's a language where you can write Java- or C#-like code with no "magic": no reflection, no AOP, none of the stuff that tends to be the biggest cause of bugs in real-world Java/C# codebases. All of the stuff that you would need reflection or AOP (or metaclasses or macros, in other languages) for, you can do in plain old Scala code.

In the abstract, it's the only mainstream language to offer both higher-kinded types and traditional OO ("extends") inheritance. From one side it offers all the good stuff of OCaml, F#, Swift, Kotlin, or Rust, but with a better type system that makes handling secondary concerns via "context-like" types a breeze. From the other side, it offers similar power to Haskell, but with more understandable performance, a better library/tool ecosystem (IDE, profiler and so on), less reliance on memory-unsafe code in practice (a lot of things in Haskell require C-wrapping libraries for things like image formats, whereas the corresponding cases in Scala wrap Java instead), and the ability to use traditional OO style if you want.

Well the oblivious answer would be Java, but I get that my contempt for it is the only thing causing me to look at Scala and that's by no means universal as most people are pretty happy with the latest versions.

Well, it's the language of choice for Spark. That fills the big data niche.