You can find two definitions/understandings of the distinction:
One, which seems (at least to me) is based on how prominent the fantastical elements are, and the works being set in a rational world. With this definition, Game of Thrones is Low Fantasy. And you probably could consider Conan a such as well. This definition was present on Wikipedia in early 2017 (and presumably before that,I didn't bother to check).
There High Fantasy has fantastical races, monsters, wizards and the like.
The other definition is based on "separation of worlds" in which "Low Fantasy" is fantasy interacting with our mundane reality; either by magic being in another world to which characters gain access, a separate "hidden" world, or magic mingling with the mundane on earth.
With High Fantasy being a fantasy set in a different world.
This puts Harry Potter and Shadowrun as Low Fantasy, while having Conan and Game of Thrones as High Fantasy.
I personally find the latter... Unnecessary, considering there is already "Urban Fantasy", "Magical Realism" and I believe "Portal Fantasy" that should cover those ranges.