It took me a moment to parse, but that snippet is actually pretty straight-forward when you know that Nim compiles down to C (or C++).

  type Vector* {.importcpp: "std::vector", header: "<vector>".}[T] = object

This obviously creates a type "Vector" whose underlying implementation is C++'s "std::vector". (I don't know how writeable it is, but it is* readable.)

  template `[]=`*[T](v: var Vector[T], key: int, val: T)

Function declaration syntax for operator overloads is hard to make readable (as in: familiar). In fact, this is about as readable as it can get (although I'm confused by the "*[T]").

  = {.emit: [v, "[", key, "] = ", val, ";"].}

As I said, when you know that the compiler generates C code, this makes a lot of sense. It's a compiler instruction to compose a string of C code.